Introduction to Type I and Type II errors

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- [Instructor] What we're
gonna do in this video

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is talk about Type I errors

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and Type II errors

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and this is in the context
of significance testing.

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So just as a little bit of review,

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in order to do a significance test,

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we first come up with a null

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and an alternative hypothesis.

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And we'll do this on some
population in question.

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This will say some hypotheses
about a true parameter

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for this population.

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And the null hypothesis
tends to be kind of

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what was always assumed or the status quo

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while the alternative hypothesis,

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hey, there's news here,

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there's something alternative here.

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And to test it, and we're really testing

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the null hypothesis.

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We're gonna decide
whether we want to reject

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or fail to reject the null hypothesis,

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we take a sample.

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We take a sample from this population.

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Using that sample, we
calculate a statistic,

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we calculate a statistic,
that's trying to estimate

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the parameter in question.

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And then using that statistic,

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we try to come up with the probability

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of getting that statistic,

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the probability of getting that statistic

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that we just calculated from that sample

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of a certain size, given
if we were to assume

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that our null hypothesis,

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if our null hypothesis is true.

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And if this probability, which
is often known as a p-value,

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is below some threshold
that we set ahead of time

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which is known as the significance level,

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then we reject the null hypothesis.

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Let me write this down.

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So this right over here,
this is our p-value.

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This should all be review,

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we introduced it in other videos.

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We have seen on other
videos if our p-value

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is less than our significance level,

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then we reject our null hypothesis,

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and if our p-value

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is greater than or equal to
our significance level, alpha,

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then we fail to reject,

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fail to reject our null hypothesis.

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And when we reject our null hypothesis,

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some people will say that might suggest

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the alternative hypothesis.

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And the reason why this makes sense is

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if the probability

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of getting the statistic from a sample

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of a certain size, if we assume

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that the null hypothesis is true

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is reasonably low if
it's below a threshold,

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maybe this threshold is 5%,

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if the probability of that
happening was less than 5%,

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then hey, maybe it's
reasonable to reject it.

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But we might be wrong in
either of these scenarios

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and that's where these
errors come into play.

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Let's make a grid to make this clear.

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So there's the reality,

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let me put reality up here,

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so the reality is there's two
possible scenarios in reality,

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one is the null hypothesis is true

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and the other is that the
null hypothesis is false,

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and then based on our significance test,

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there's two things that we might do,

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we might reject the null hypothesis,

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or we might fail to

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reject the null hypothesis.

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And so let's put a little grid here

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to think about the different combinations,

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the different scenarios here.

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So in a scenario where the
null hypothesis is true,

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but we reject it, that
feels like an error.

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We shouldn't reject something that is true

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and that indeed is a Type I error.

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Type I error.

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You shouldn't reject the null
hypothesis if it was true.

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And you can even figure
out what is the probability

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of getting a Type I error.

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Well that's gonna be
your significance level

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because if your null hypothesis is true,

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let's say that your
significance level is 5%,

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well 5% of the time, even if
your null hypothesis is true,

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you're going to get a statistic

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that's going to make you
reject the null hypothesis.

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So one way to think about the
probability of a Type I error

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is your significance level.

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Now, if your null hypothesis is true

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and you failed to reject
it, well that's good.

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This we can write this as,
this is a correct conclusion.

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The good thing just happened
to happen this time.

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Now, if your null hypothesis
is false and you reject it,

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that's also good.

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That is the correct conclusion.

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But if your null hypothesis is false

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and you failed to reject it, well then

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that is a Type II error.

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That is a Type II error.

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Now with this context,
in the next few videos,

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we will actually do some examples

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where we try to identify,

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one, whether an error is occurring

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and whether that error
is a Type I or a Type II.


Estimating a P-value from a simulation

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- [Instructor] So we have a
question here on p-values.

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It says Evie read an article that said 6%

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of teenagers were vegetarians,

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but she thinks it's higher
for students at her school.

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To test her theory, Evie
took a random sample

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of 25 students at her school,

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and 20% of them were vegetarians.

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So just from this first paragraph,

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some interesting things are being said.

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It's saying that the true
population proportion,

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if we believe this article, of teenagers

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that are vegetarian,

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we could say that is 6%.

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Now for her school, there
is a null hypothesis

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that the proportion of
students at her school

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that are vegetarian, so
this is at her school,

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that the true proportion,
the null would be as

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the same as the proportion
of teenagers as a whole.

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So that would be the null hypothesis.

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And you can see that she's generating

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an alternative hypothesis,

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but she thinks it's higher for
students at her large school.

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So her alternative hypothesis
would be the proportion,

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the true population
parameter for her school

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is greater than 6%.

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And so to see whether
or not you could reject

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the null hypothesis, you take a sample,

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and that's exactly what Evie did.

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She took a random sample of 25 students,

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and you calculate the sample proportion.

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And then you figure out
what is the probability

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of getting a sample proportion
this high or greater?

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And if it's lower than a threshold,

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then you will reject your null hypothesis.

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And that probability we call the p-value.

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The p-value is equal to

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the probability that
your sample proportion,

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as she's doing this for
students at her school,

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is going to be greater
than or equal to 20%

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if you assumed that your
null hypothesis was true.

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So if you assumed that the true proportion

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at your school was 6% vegetarians,

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but you took a sample of 25 students

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where you got 20%, what is the probability

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of getting 20% or greater
for a sample of 25?

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Now there's many ways to approach it

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but it looks like she
is using a simulation.

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To see how likely a sample like this

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was to happen by random chance alone,

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Evie performed a simulation.

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She simulated 40 samples
of n equals 25 students

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from a large population where 6%

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of the students were vegetarian.

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She recorded the proportion
of vegetarians in each sample.

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Here are the sample proportions
from her 40 samples.

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So what she's doing here
with the simulation,

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this is an approximation of
the sampling distribution

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of the sample proportions
if you were to assume

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that your null hypothesis is true.

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And it says below,

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Evie wants to test her null hypothesis

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which is that the true
proportion at her school is 6%

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versus the alternative hypothesis

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that the true proportion at
her school is greater than 6%

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where p is the true proportion of students

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who are vegetarian at her school.

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And then they ask us,

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based on these simulated results,

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what is the approximate
p-value of the test?

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And they say, the sample result,

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the sample proportion here, was 20%,

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we saw that right over here.

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Well if we assumed that this

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is a reasonably good approximation

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of our sampling distribution
of our sample proportions,

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there's 40 data points here,

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and how many of these samples
do we get a sample proportion

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that is greater than or equal to 20%?

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Well you could see this
is 20% right over here,

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20 hundredths, and so
you see we have three

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right over here that meet this constraint.

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And so that is three out of 40.

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So if we think this is a
reasonably good approximation,

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we would say that our p-value

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is going to be approximately

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three out of 40, that
if the true population

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proportion for the school were 6%,

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if the null hypothesis were true,

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then approximately three
out of every 40 times

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you would expect to get a sample

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with 20% or larger being vegetarians.

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And so three-fortieths is what?

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Let's see, if I multiply
both the numerator

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and denominator by two and a half,

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this is approximately equal to,

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I say two and a half 'cause
to go from 40 to 100,

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and then two and a half
times three would be 7.5.

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So would say this is approximately 7.5%

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and this is actually a
multiple choice question

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and if we scroll down,

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we do indeed see

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approximately 7.5% right over there.


P-values and significance tests

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- Let's say that I run a website

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that currently has this off white color

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for it's background

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and I know the mean amount of time

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that people spend on my website,

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let's say it is 20 minutes

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and I'm interested in making a change

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that will make people spend
more time on my website.

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My idea is to make the background color

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of my website yellow.

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But after making that change,

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how do I feel good about
this actually having

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the intended consequence?

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Well that's where significance
tests come into play.

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What I would do is first
set up some hypotheses,

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a null hypothesis and an
alternative hypothesis.

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The null hypothesis tends
to be a statement that,

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"Hey, your change actually had no effect,

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"there's no news here,"
and so this would be that

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your mean is still equal to 20 minutes

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after the change to yellow, in this case,

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for our background.

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And we would also have an
alternative hypothesis.

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Our alternative hypothesis is actually

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that our mean is now greater
because of the change,

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that people are spending
more time on my site.

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So our mean is greater than
20 minutes after the change.

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Now the next thing we do is we set up

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a threshold known as
the significance level

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and you will see how this
comes into play in a second.

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So, your significance level

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is usually denoted by
the Greek letter Alpha

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and you tend to see
significant levels like

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1/100 or 5/100 or 1/10

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or 1%, 5%, or 10%.

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You might see other ones,

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but we're gonna set a significance level

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for this particular case.

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Let's just say it's going to be 0.05.

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And what we're going to
now do is we're going to

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take a sample of people visiting

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this new yellow background website

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and we're gonna calculate statistics.

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The sample mean, the
sample standard deviation,

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and we're gonna say,
"Hey, if we assume that

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"the null hypothesis is true,

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"what is the probability
of getting a sample

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"with the statistics that we get?"

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And if that probability is lower than

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our significance level,

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if that probability is less than 5/100,

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if it's less than 5%, then
we reject the null hypothesis

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and say that we have
evidence for the alternative.

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However, if the probability
of getting the statistics

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for that sample are at the
significance level or higher,

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then we say, "Hey, we can't
reject the null hypothesis,

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"and we aren't able to have
evidence for the alternative."

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So what we would then do, I
will call this step three.

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In step three, we would take a sample.

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So let's say we take a sample size,

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let's say we take 100 folks
who visit the new website,

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the yellow background website,

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and we measure sample statistics.

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We measure the sample mean here,

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let's say that for that sample,

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the mean is 25 minutes.

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We are also likely to,

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if we don't know what the actual

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population standard deviation is,

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which we typically don't know,

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we would also calculate the
sample standard deviation.

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Then the next step is
we calculate a p-value.

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And the p-value, which
stands for probability value,

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is the probability of getting a statistic

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at least this far away from the mean

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if we were to assume that
the null hypothesis is true.

00:03:42.300 --> 00:03:43.681
So one way to think about it

00:03:43.681 --> 00:03:45.419
it is a conditional probability.

00:03:45.419 --> 00:03:49.586
It is the probability that our sample mean

00:03:50.561 --> 00:03:53.550
when we take a sample of size n=100

00:03:53.550 --> 00:03:57.380
is greater than or equal to 25 minutes,

00:03:59.170 --> 00:04:03.337
given our null hypothesis is true.

00:04:05.600 --> 00:04:08.700
And in other videos, we have
talked about how to do this.

00:04:08.700 --> 00:04:11.030
If we assume that the
sampling distribution

00:04:11.030 --> 00:04:14.130
of the sample means is roughly normal,

00:04:14.130 --> 00:04:15.930
we can use the sample mean,

00:04:15.930 --> 00:04:17.550
we can use our sample size,

00:04:17.550 --> 00:04:19.720
we can use our sample standard deviation,

00:04:19.720 --> 00:04:21.590
perhaps we use a t-statistic,

00:04:21.590 --> 00:04:25.050
to figure out what this
probability is going to be.

00:04:25.050 --> 00:04:27.340
And then we decide whether we can reject

00:04:27.340 --> 00:04:28.560
the null hypothesis.

00:04:28.560 --> 00:04:31.110
So let me call that step five.

00:04:31.110 --> 00:04:34.250
So step five, there are two situations.

00:04:34.250 --> 00:04:38.417
If my p-value, if it is less than Alpha,

00:04:41.600 --> 00:04:45.600
then I reject my null hypothesis

00:04:49.760 --> 00:04:54.330
and say that I have evidence
for my alternative hypothesis.

00:04:54.330 --> 00:04:56.440
Now, if we have the other situation,

00:04:56.440 --> 00:05:00.607
if my p-value is greater than or equal to,

00:05:02.030 --> 00:05:04.120
in this case 0.05,

00:05:05.130 --> 00:05:09.800
so if it's greater than or
equal to my significance level,

00:05:09.800 --> 00:05:12.830
then I cannot reject the null hypothesis.

00:05:12.830 --> 00:05:15.210
I wouldn't say that I
accept the null hypothesis,

00:05:15.210 --> 00:05:17.560
I would just say that we do not

00:05:20.651 --> 00:05:24.690
reject the null hypothesis.

00:05:24.690 --> 00:05:28.330
And so, let's say, when I do
all of these calculations,

00:05:28.330 --> 00:05:31.700
I get a p-value which would
put me in this scenario

00:05:31.700 --> 00:05:32.610
right over here.

00:05:32.610 --> 00:05:36.670
Let's say that I get a p-value of 0.03.

00:05:38.389 --> 00:05:42.550
0.03 is indeed less than 0.05

00:05:42.550 --> 00:05:44.900
so I would reject the null hypothesis

00:05:44.900 --> 00:05:48.060
and say that I have evidence
for the alternative.

00:05:48.060 --> 00:05:50.333
And this should hopefully
make logical sense

00:05:50.333 --> 00:05:51.960
because what we're saying is, hey, look,

00:05:51.960 --> 00:05:55.120
we took a sample and if we
assume the null hypothesis,

00:05:55.120 --> 00:05:59.287
the probability of getting
that sample is 3%, it's 3/100,

00:06:01.070 --> 00:06:02.750
and so since that probability

00:06:02.750 --> 00:06:05.210
is less than our
probability threshold here,

00:06:05.210 --> 00:06:07.190
we'll reject it and say we have evidence

00:06:07.190 --> 00:06:08.400
for the alternative.

00:06:08.400 --> 00:06:10.660
On the other hand, there
might have been a scenario

00:06:10.660 --> 00:06:13.130
where we do all of the calculations here

00:06:13.130 --> 00:06:17.750
and we figure out a p-value that we get

00:06:17.750 --> 00:06:21.917
is equal to 0.5, which you
can interpret as saying

00:06:22.940 --> 00:06:26.430
that hey, if we assume the
null hypothesis is true,

00:06:26.430 --> 00:06:30.000
that there's no change due to
making the background yellow,

00:06:30.000 --> 00:06:33.770
I would have a 50% chance
of getting this result.

00:06:33.770 --> 00:06:36.110
And in that situation,
since it's higher than

00:06:36.110 --> 00:06:37.290
my significance level,

00:06:37.290 --> 00:06:39.060
I wouldn't reject the null hypothesis.

00:06:39.060 --> 00:06:41.260
A world where the null hypothesis is true

00:06:41.260 --> 00:06:42.220
and I get this result,

00:06:42.220 --> 00:06:45.680
well, you know, it
seems reasonably likely.

00:06:45.680 --> 00:06:49.850
And so, this is the basis for
significant tests generally

00:06:49.850 --> 00:06:53.832
and as you'll see, is
applicable in almost every field

00:06:53.832 --> 00:06:55.960
you'll find yourself in.

00:06:55.960 --> 00:06:57.930
Now there's one last
point of clarification

00:06:57.930 --> 00:07:00.430
that I wanna make very, very, very clear.

00:07:00.430 --> 00:07:02.680
Our p-value, the thing that we're using

00:07:02.680 --> 00:07:06.480
to decide whether or not we
reject the null hypothesis,

00:07:06.480 --> 00:07:09.555
this is the probability of
getting your sample statistics

00:07:09.555 --> 00:07:13.000
given that the null hypothesis is true.

00:07:13.000 --> 00:07:15.200
Sometimes people confuse
this and they say,

00:07:15.200 --> 00:07:18.280
"Hey, is this the probability
that the null hypothesis

00:07:18.280 --> 00:07:22.447
"is true given the sample
statistics that we got?"

00:07:27.130 --> 00:07:30.000
And I would say, "Clearly,
no, that is not the case."

00:07:30.000 --> 00:07:32.020
We are not trying to gauge the probability

00:07:32.020 --> 00:07:34.940
that the null hypothesis is true or not.

00:07:34.940 --> 00:07:36.720
What we are trying to do is say,

00:07:36.720 --> 00:07:40.330
"Hey, if we assume the
null hypothesis were true,

00:07:40.330 --> 00:07:43.110
"what is the probability
that we got the result

00:07:43.110 --> 00:07:44.830
"that we did for our sample?"

00:07:44.830 --> 00:07:46.580
And if that probability is low,

00:07:46.580 --> 00:07:50.070
if it's below some threshold
that we set ahead of time,

00:07:50.070 --> 00:07:53.560
then we decide to reject
the null hypothesis

00:07:53.560 --> 00:07:56.880
and say that we have
evidence for the alternative.


Examples of null and alternative hypotheses

WEBVTT
Kind: captions
Language: en

00:00:00.190 --> 00:00:02.740
- [Instructor] We are told
a restaurant owner installed

00:00:02.740 --> 00:00:05.240
a new automated drink machine.

00:00:05.240 --> 00:00:09.230
The machine is designed to
dispense 530 milliliters

00:00:09.230 --> 00:00:12.130
of liquid on the medium size setting.

00:00:12.130 --> 00:00:15.640
The owner suspects that the
machine may be dispensing

00:00:15.640 --> 00:00:17.990
too much in medium drinks.

00:00:17.990 --> 00:00:20.980
They decide to take a
sample of 30 medium drinks

00:00:20.980 --> 00:00:22.900
to see if the average amount

00:00:22.900 --> 00:00:26.690
is significantly greater
than 500 milliliters.

00:00:26.690 --> 00:00:29.620
What are appropriate hypotheses for their

00:00:29.620 --> 00:00:30.910
significance test?

00:00:30.910 --> 00:00:33.100
And they actually give
us four choices here.

00:00:33.100 --> 00:00:35.303
I'll scroll down a little
bit so that you can see

00:00:35.303 --> 00:00:37.210
all of the choices.

00:00:37.210 --> 00:00:39.230
So like always, pause
this video and see if you

00:00:39.230 --> 00:00:40.250
can have a go at it.

00:00:41.300 --> 00:00:42.970
Okay now let's do this together.

00:00:42.970 --> 00:00:46.830
So let's just remind ourselves
what a null hypothesis is

00:00:46.830 --> 00:00:49.640
and what an alternative hypothesis is.

00:00:49.640 --> 00:00:51.730
One way to view a null hypothesis,

00:00:51.730 --> 00:00:53.350
this is the hypothesis where

00:00:53.350 --> 00:00:55.110
things are happening as expected.

00:00:55.110 --> 00:00:56.550
Sometimes people will describe this

00:00:56.550 --> 00:00:58.810
as the no difference hypothesis.

00:00:58.810 --> 00:01:02.240
It'll often have a
statement of equality where

00:01:02.240 --> 00:01:03.841
the population parameter

00:01:03.841 --> 00:01:06.650
is equal to a value
where the value is what

00:01:06.650 --> 00:01:09.610
people were kind of assuming all along.

00:01:09.610 --> 00:01:11.630
The alternative hypothesis,

00:01:11.630 --> 00:01:14.190
this is a claim where if you have evidence

00:01:14.190 --> 00:01:15.110
to back up that claim,

00:01:15.110 --> 00:01:16.810
that would be new news.

00:01:16.810 --> 00:01:18.970
You are saying hey there's
something interesting

00:01:18.970 --> 00:01:19.803
going on here.

00:01:19.803 --> 00:01:21.200
There is a difference.

00:01:21.200 --> 00:01:22.760
And so in this context,

00:01:22.760 --> 00:01:24.090
the no difference,

00:01:24.090 --> 00:01:26.470
we would say the null hypothesis would be,

00:01:26.470 --> 00:01:28.790
we would care about the
population parameter,

00:01:28.790 --> 00:01:31.060
and here we care about the
average amount of drink

00:01:31.060 --> 00:01:33.130
dispensed in the medium setting.

00:01:33.130 --> 00:01:36.050
So the population parameter
there would be the mean,

00:01:36.050 --> 00:01:39.780
and that the mean would be
equal to 530 milliliters.

00:01:39.780 --> 00:01:43.660
Because that's what the drink
machine is supposed to do.

00:01:43.660 --> 00:01:45.420
And then the alternative hypothesis,

00:01:45.420 --> 00:01:46.980
this is what the owner fears,

00:01:46.980 --> 00:01:50.130
is that the mean actually
might be larger than that,

00:01:50.130 --> 00:01:53.210
larger than 530 milliliters.

00:01:53.210 --> 00:01:55.950
And so let's see which
of these choices is this?

00:01:55.950 --> 00:01:58.250
Well these first two choices
are talking about proportion,

00:01:58.250 --> 00:02:00.860
but it's really the average
amount that we're talking about.

00:02:00.860 --> 00:02:02.970
We see it up here.

00:02:02.970 --> 00:02:04.880
They decide to take a
sample of 30 medium drinks

00:02:04.880 --> 00:02:06.700
to see if the average amount,

00:02:06.700 --> 00:02:07.940
they're not talking
about proportions here,

00:02:07.940 --> 00:02:09.600
they're talking about averages,

00:02:09.600 --> 00:02:12.080
and in this case we're
talking about estimating

00:02:12.080 --> 00:02:15.010
the population parameter,
the population mean,

00:02:15.010 --> 00:02:18.450
for how much drink is
dispensed on that setting.

00:02:18.450 --> 00:02:23.310
And so this one is looking
like this right over here.

00:02:23.310 --> 00:02:25.920
Only these two are even
dealing with the mean.

00:02:25.920 --> 00:02:27.930
And the difference between
this one and this one

00:02:27.930 --> 00:02:30.970
is this says the mean is
greater than 530 milliliters,

00:02:30.970 --> 00:02:33.450
and that indeed is the owner's fear.

00:02:33.450 --> 00:02:35.590
And this over here, this
alternative hypothesis,

00:02:35.590 --> 00:02:37.810
is that the, that it's
dispensing on average

00:02:37.810 --> 00:02:39.520
less than 530 milliliters,

00:02:39.520 --> 00:02:41.810
but that's not what
the owner is afraid of.

00:02:41.810 --> 00:02:44.010
And so that's not the kind of the news

00:02:44.010 --> 00:02:46.140
that we're trying to
find some evidence for.

00:02:46.140 --> 00:02:48.840
So I would definitely pick choice C.

00:02:48.840 --> 00:02:50.090
Let's do another example.

00:02:51.050 --> 00:02:53.580
The National Sleep Foundation recommends

00:02:53.580 --> 00:02:57.170
that teenagers aged 14 to 17 years old

00:02:57.170 --> 00:02:59.910
get at least eight
hours of sleep per night

00:02:59.910 --> 00:03:02.410
for proper health and wellness.

00:03:02.410 --> 00:03:05.370
A statistics class at a
large high school suspects

00:03:05.370 --> 00:03:07.185
that students at their school are getting

00:03:07.185 --> 00:03:11.860
less than eight hours of sleep on average.

00:03:11.860 --> 00:03:13.480
To test their theory,

00:03:13.480 --> 00:03:16.300
they randomly sample 42 of these students

00:03:16.300 --> 00:03:20.120
and ask them how many hours
of sleep they get per night.

00:03:20.120 --> 00:03:22.160
The mean from this sample,

00:03:22.160 --> 00:03:23.500
the mean from the sample,

00:03:23.500 --> 00:03:26.010
is 7.5 hours.

00:03:26.010 --> 00:03:28.610
Here's their alternative hypothesis.

00:03:28.610 --> 00:03:31.430
The average amount of sleep
students at their school get

00:03:31.430 --> 00:03:33.520
per night is...

00:03:33.520 --> 00:03:35.230
What is an appropriate ending

00:03:35.230 --> 00:03:36.950
to their alternative hypothesis?

00:03:36.950 --> 00:03:40.330
So pause this video and see
if you can think about that.

00:03:40.330 --> 00:03:43.470
So let's just first think
about a good null hypothesis.

00:03:43.470 --> 00:03:45.010
So the null hypothesis is,

00:03:45.010 --> 00:03:47.200
hey there's actually no news here,

00:03:47.200 --> 00:03:50.110
that everything is what
people were always assuming.

00:03:50.110 --> 00:03:51.490
And so the null hypothesis
here is that no,

00:03:53.510 --> 00:03:55.960
the students are getting
at least eight hours

00:03:55.960 --> 00:03:57.140
of sleep per night.

00:03:57.140 --> 00:03:58.950
And so that would be,

00:03:58.950 --> 00:04:02.390
that remember we care about
the population of students.

00:04:02.390 --> 00:04:04.850
And so and we care about
the population of students

00:04:04.850 --> 00:04:06.360
at the school.

00:04:06.360 --> 00:04:08.630
And so we would say
well the null hypothesis

00:04:08.630 --> 00:04:11.510
is that the parameter for
the students at that school,

00:04:11.510 --> 00:04:13.400
the mean amount of sleep
that they're getting,

00:04:13.400 --> 00:04:17.070
is indeed greater than
or equal to eight hours.

00:04:18.620 --> 00:04:21.750
And a good clue for the
alternative hypothesis

00:04:21.750 --> 00:04:24.380
is when you see something
like this where they say,

00:04:24.380 --> 00:04:27.210
a statistics class at a
large high school suspects,

00:04:27.210 --> 00:04:29.530
so they suspect that
things might be different

00:04:29.530 --> 00:04:31.250
than what people have always been assuming

00:04:31.250 --> 00:04:32.840
or actually what's good for students.

00:04:32.840 --> 00:04:35.020
And so they suspect that
students at their school

00:04:35.020 --> 00:04:38.430
are getting less than eight
hours of sleep on average.

00:04:38.430 --> 00:04:41.510
And so they suspect that
the population parameter,

00:04:41.510 --> 00:04:45.100
the population mean, for
their school is actually

00:04:45.100 --> 00:04:48.170
less than eight hours.

00:04:48.170 --> 00:04:50.653
And so if you wanted to write this

00:04:50.653 --> 00:04:52.030
out in words,

00:04:52.030 --> 00:04:54.890
the average amount of sleep
students at their school get

00:04:54.890 --> 00:04:58.190
per night is less

00:04:58.190 --> 00:05:01.660
than eight hours.

00:05:01.660 --> 00:05:03.960
Now one thing to watch out for is one,

00:05:03.960 --> 00:05:06.187
you wanna make sure you're
getting the right parameter.

00:05:06.187 --> 00:05:09.120
Sometimes it's often a population mean.

00:05:09.120 --> 00:05:11.550
Sometimes it's a population proportion.

00:05:11.550 --> 00:05:13.580
But the other thing that sometimes

00:05:13.580 --> 00:05:15.610
folks get stuck up on,

00:05:16.510 --> 00:05:19.030
but the other thing that
sometimes confuses folks is,

00:05:19.030 --> 00:05:21.410
well we are measuring,

00:05:21.410 --> 00:05:23.380
is that we are calculating a statistic

00:05:23.380 --> 00:05:24.490
from a sample.

00:05:24.490 --> 00:05:27.400
Here we're calculating the sample mean,

00:05:27.400 --> 00:05:30.080
but that, the sample
statistics are not what

00:05:30.080 --> 00:05:32.690
should be involved in your hypotheses.

00:05:32.690 --> 00:05:36.930
Your hypotheses are claims
about your population

00:05:36.930 --> 00:05:37.763
that you care about,

00:05:37.763 --> 00:05:41.787
here the population is the
students at the high school.


Diagramming how a bill becomes a law in the U.S.

WEBVTT
Kind: captions
Language: en

00:00:00.380 --> 00:00:01.230
- [Instructor] What we're
going to do in this video

00:00:01.230 --> 00:00:04.260
is diagram out how a
bill can become a law.

00:00:04.260 --> 00:00:06.850
And I make a distinction
between a non-tax bill

00:00:06.850 --> 00:00:09.327
and a tax bill because a non-tax bill

00:00:09.327 --> 00:00:13.560
can be introduced into either
chamber of Congress initially.

00:00:13.560 --> 00:00:15.720
It can be introduced into the Senate

00:00:15.720 --> 00:00:17.730
or it can be introduced into the

00:00:17.730 --> 00:00:19.190
House of Representatives.

00:00:19.190 --> 00:00:21.760
While something that deals with taxation

00:00:21.760 --> 00:00:24.920
can only be introduced initially

00:00:24.920 --> 00:00:28.070
into the House of Representatives.

00:00:28.070 --> 00:00:30.330
And as we've talked about in other videos,

00:00:30.330 --> 00:00:33.140
anyone can be involved
in the drafting of a bill

00:00:33.140 --> 00:00:34.880
but it actually needs
to be introduced into

00:00:34.880 --> 00:00:37.850
the appropriate chamber by
a member of that chamber.

00:00:37.850 --> 00:00:41.040
But let's say that it gets
introduced into the Senate,

00:00:41.040 --> 00:00:42.540
what happens then?

00:00:42.540 --> 00:00:45.820
Well it will be referred to
the appropriate committee

00:00:45.820 --> 00:00:47.300
and what is the appropriate committee?

00:00:47.300 --> 00:00:48.780
Well if it deals with foreign relations

00:00:48.780 --> 00:00:50.410
it would go to the Foreign
Relations Committee.

00:00:50.410 --> 00:00:52.620
If it deals with the Armed Services,

00:00:52.620 --> 00:00:55.460
well it would go to the
Armed Services Committee.

00:00:55.460 --> 00:00:57.270
You get the general idea.

00:00:57.270 --> 00:00:59.290
Now in the committee
they might have hearings,

00:00:59.290 --> 00:01:00.580
they might debate it

00:01:00.580 --> 00:01:02.210
and if they decide to debate it

00:01:02.210 --> 00:01:03.310
and have a vote on it,

00:01:03.310 --> 00:01:04.640
it could pass.

00:01:04.640 --> 00:01:07.880
So lets say it passes
through the committee,

00:01:07.880 --> 00:01:09.440
and then the majority leader,

00:01:09.440 --> 00:01:10.710
and the majority leader is the

00:01:10.710 --> 00:01:13.040
leader of the majority
party in the Senate.

00:01:13.040 --> 00:01:15.290
They have a lot of influence on how

00:01:15.290 --> 00:01:19.620
and when that bills gets
debated on the Senate floor.

00:01:19.620 --> 00:01:21.630
But lets say they schedule it for debate

00:01:21.630 --> 00:01:23.110
on the Senate floor.

00:01:23.110 --> 00:01:26.450
Once things get to a
vote on the Senate floor

00:01:26.450 --> 00:01:29.570
they need a simple majority to pass.

00:01:29.570 --> 00:01:32.090
So lets say that this bill passes

00:01:32.090 --> 00:01:33.150
and I know what you're thinking.

00:01:33.150 --> 00:01:34.280
You might have heard numbers like

00:01:34.280 --> 00:01:37.170
60 out of 100 votes or 2/3 majority.

00:01:37.170 --> 00:01:40.540
Where the 2/3 is necessary
to ratify a treaty,

00:01:40.540 --> 00:01:43.710
the 60 votes that's necessary for cloture,

00:01:43.710 --> 00:01:45.480
to end most filibusters.

00:01:45.480 --> 00:01:47.990
And so functionally it often does require

00:01:47.990 --> 00:01:50.610
more than a simple majority support

00:01:50.610 --> 00:01:53.580
in order to get even to a vote.

00:01:53.580 --> 00:01:54.810
But lets say that this bill,

00:01:54.810 --> 00:01:57.430
that was initially
introduced into the Senate

00:01:57.430 --> 00:01:59.710
makes it all the way through.

00:01:59.710 --> 00:02:01.630
What happens then?

00:02:01.630 --> 00:02:03.450
Well if there isn't a similar bill

00:02:03.450 --> 00:02:05.710
that was introduced into
the House of Representatives

00:02:05.710 --> 00:02:07.730
and got through the
House of Representatives

00:02:07.730 --> 00:02:08.990
this bill would then go through

00:02:08.990 --> 00:02:11.240
a similar process in the House.

00:02:11.240 --> 00:02:14.910
So then this bill would go all the way,

00:02:14.910 --> 00:02:17.790
it would be introduced into
the House of Representatives.

00:02:17.790 --> 00:02:21.060
It would be referred to
the appropriate committee

00:02:21.060 --> 00:02:24.790
and then once it passes through
the appropriate committee

00:02:24.790 --> 00:02:26.830
it would go through the Rules Committee.

00:02:26.830 --> 00:02:29.380
And the Rules Committee
is one of these major

00:02:29.380 --> 00:02:31.750
distinctions between the
House and the Senate.

00:02:31.750 --> 00:02:33.730
The Senate does have a Rules Committee

00:02:33.730 --> 00:02:35.770
but it is nowhere near as powerful.

00:02:35.770 --> 00:02:38.780
In the House the Rules
Committee can control a lot.

00:02:38.780 --> 00:02:40.670
It can decide when and how

00:02:40.670 --> 00:02:43.900
or even whether a bill
even gets to the floor.

00:02:43.900 --> 00:02:47.000
But lets say that it does get to the floor

00:02:47.000 --> 00:02:49.380
and then it gets a simple majority

00:02:49.380 --> 00:02:51.910
of the House members to vote for it.

00:02:51.910 --> 00:02:56.400
Well then this bill would
then go to the President.

00:02:56.400 --> 00:02:58.130
Now some interesting things happen

00:02:58.130 --> 00:02:59.870
once it gets to the President.

00:02:59.870 --> 00:03:03.270
The President can of course
decide sign the bill.

00:03:03.270 --> 00:03:05.330
So then sign the bill,

00:03:05.330 --> 00:03:09.160
in which case that bill will become law.

00:03:09.160 --> 00:03:13.470
The President could also
decide to veto the bill.

00:03:13.470 --> 00:03:15.560
Now if the President vetoes the bill,

00:03:15.560 --> 00:03:19.600
it would go back to the
chamber in which it originated.

00:03:19.600 --> 00:03:22.010
In this first example
that we're talking about

00:03:22.010 --> 00:03:25.369
that vetoed bill would
go back to the Senate.

00:03:25.369 --> 00:03:28.530
And in order to override the veto

00:03:28.530 --> 00:03:31.110
they would need a 2/3 majority.

00:03:31.110 --> 00:03:34.920
And even if they where able to
get the 2/3 right over here,

00:03:34.920 --> 00:03:36.580
it's still wouldn't become a law.

00:03:36.580 --> 00:03:39.950
Then it would have to
get the 2/3 in the House.

00:03:39.950 --> 00:03:42.600
But if it was able to get
the 2/3 there as well,

00:03:42.600 --> 00:03:45.700
well then they have overwritten
the President's veto

00:03:45.700 --> 00:03:48.780
and it will become a law.

00:03:48.780 --> 00:03:51.700
Now there's other edge cases
that involve the President.

00:03:51.700 --> 00:03:54.850
If a President does nothing for 10 days,

00:03:54.850 --> 00:03:58.000
and if Congress is in
session for those 10 days,

00:03:58.000 --> 00:04:00.520
well then it can become a law.

00:04:00.520 --> 00:04:04.687
So nothing for 10 days,

00:04:06.390 --> 00:04:09.000
well then you can also make it a law.

00:04:09.000 --> 00:04:11.800
And there's also called a pocket veto,

00:04:11.800 --> 00:04:13.690
where the President does nothing

00:04:13.690 --> 00:04:15.940
but the Congress goes out of session

00:04:15.940 --> 00:04:17.670
within that 10 days.

00:04:17.670 --> 00:04:18.810
And so let me do this.

00:04:18.810 --> 00:04:22.977
This would be a pocket
veto right over here

00:04:23.980 --> 00:04:25.540
and I'll just put that in quotes

00:04:25.540 --> 00:04:28.760
because that's also the
President doing nothing

00:04:28.760 --> 00:04:33.130
but Congress goes out of
session within those 10 days.

00:04:33.130 --> 00:04:34.830
Now one thing to be clear,

00:04:34.830 --> 00:04:37.620
even what I've drawn
here is a simplification.

00:04:37.620 --> 00:04:39.360
There many steps in this process

00:04:39.360 --> 00:04:40.880
where bill could change,

00:04:40.880 --> 00:04:43.010
where a bill could die

00:04:43.010 --> 00:04:46.630
or a bill could just go into
some sort of a limbo state.

00:04:46.630 --> 00:04:51.080
For example, a committee
can decide to add to a bill

00:04:51.080 --> 00:04:53.670
that would be called amending a bill.

00:04:53.670 --> 00:04:55.530
So that could happen over there.

00:04:56.867 --> 00:04:58.340
That can actually happen other places.

00:04:59.234 --> 00:05:01.670
Maybe a bill does not
pass through committee.

00:05:01.670 --> 00:05:02.770
Not pass.

00:05:02.770 --> 00:05:05.950
Maybe it does not pass
through the floor action.

00:05:05.950 --> 00:05:09.970
Maybe it doesn't pass the House Committee.

00:05:09.970 --> 00:05:12.440
Maybe it doesn't pass through the House.

00:05:12.440 --> 00:05:17.220
All of these places are
where a bill could die.

00:05:17.220 --> 00:05:19.130
There's also situations where a committee

00:05:19.130 --> 00:05:21.660
could decide to table a bill.

00:05:21.660 --> 00:05:25.230
Which is not saying that
we have voted against it

00:05:25.230 --> 00:05:26.930
but they're saying hey we're
not even going to vote on it

00:05:26.930 --> 00:05:28.740
and it just goes into
a little bit of limbo

00:05:28.740 --> 00:05:30.680
but essentially the bill will die there.

00:05:30.680 --> 00:05:34.571
So it could get tabled in
committee in either chamber.

00:05:34.571 --> 00:05:38.100
Even the Rules Committee
could decide to table it.

00:05:38.100 --> 00:05:41.850
So it'd never really makes its
way to a vote on the floor.

00:05:41.850 --> 00:05:43.230
Now it's also important to note

00:05:43.230 --> 00:05:44.590
that in the example we gave,

00:05:44.590 --> 00:05:45.880
a bill started in the Senate.

00:05:45.880 --> 00:05:47.050
Made it's way through the Senate

00:05:47.050 --> 00:05:48.820
and then had to make it's
way through the House

00:05:48.820 --> 00:05:51.060
and eventually got to
the President's desk.

00:05:51.060 --> 00:05:52.560
It could have gone the other way.

00:05:52.560 --> 00:05:54.890
It could have started in the
House of Representatives.

00:05:54.890 --> 00:05:57.290
In fact if it's a tax bill
it would have had to start

00:05:57.290 --> 00:05:58.510
in the House of Representatives

00:05:58.510 --> 00:06:00.380
and if it got all the
way through the House

00:06:00.380 --> 00:06:01.790
then it would have gone into the Senate.

00:06:01.790 --> 00:06:03.730
It would have to go all
the way through the Senate

00:06:03.730 --> 00:06:06.000
and then it would end up
on the President's desk.

00:06:06.000 --> 00:06:08.260
And often times you have a situation

00:06:08.260 --> 00:06:11.090
where two parallel bills
are making their way

00:06:11.090 --> 00:06:12.440
through each chamber.

00:06:12.440 --> 00:06:14.590
So there could be a bill
that's making it's way

00:06:14.590 --> 00:06:16.400
through the Senate on say immigration

00:06:16.400 --> 00:06:18.820
and there could be a
parallel bill on immigration

00:06:18.820 --> 00:06:21.160
making it's way through the
House of Representatives.

00:06:21.160 --> 00:06:22.750
Now if each of those bills

00:06:22.750 --> 00:06:25.010
get through their respective chambers,

00:06:25.010 --> 00:06:29.177
then they go to something
called a conference committee.

00:06:32.470 --> 00:06:34.370
Which is a place where
both Representatives

00:06:34.370 --> 00:06:37.010
and Senators of the appropriate committees

00:06:37.010 --> 00:06:41.310
will get together and make
their bills gel together.

00:06:41.310 --> 00:06:43.000
Now even if they're able to agree

00:06:43.000 --> 00:06:45.700
to a unified bill so to speak,

00:06:45.700 --> 00:06:49.560
one that syncs the two bills
that went through both chambers

00:06:49.560 --> 00:06:52.650
then that synced bill would
once again have to go through

00:06:52.650 --> 00:06:54.340
both chambers again.

00:06:54.340 --> 00:06:57.050
So its' not like the conference
committee can just decide.

00:06:57.050 --> 00:07:00.690
And even what I've drawn
here is a simplification.

00:07:00.690 --> 00:07:01.840
There's all of this,

00:07:01.840 --> 00:07:03.840
whether you consider
it interesting or not,

00:07:03.840 --> 00:07:06.600
parliamentary procedure and nuances

00:07:06.600 --> 00:07:08.330
that allow different players

00:07:08.330 --> 00:07:10.670
especially the leadership
in each of the houses

00:07:10.670 --> 00:07:12.250
to have a lot of levers to either

00:07:12.250 --> 00:07:14.140
accelerate the passage of a bill

00:07:14.140 --> 00:07:16.310
or to kill it in different ways.


Senate filibusters and cloture

WEBVTT
Kind: captions
Language: en

00:00:00.540 --> 00:00:02.100
- [Instructor] What we are
going to do in this video

00:00:02.100 --> 00:00:04.420
is discuss the United States Senate.

00:00:04.420 --> 00:00:06.450
We're gonna focus not only areas

00:00:06.450 --> 00:00:08.310
where the Senate has special influence,

00:00:08.310 --> 00:00:10.560
where the House of
Representatives does not,

00:00:10.560 --> 00:00:12.150
but we'll also focus on

00:00:12.150 --> 00:00:14.550
how the Senate actually conducts business.

00:00:14.550 --> 00:00:16.120
As we'll see the processes

00:00:16.120 --> 00:00:18.060
and the rules that the Senate uses,

00:00:18.060 --> 00:00:21.080
makes it more difficult
for simple majority

00:00:21.080 --> 00:00:22.740
to do what they want.

00:00:22.740 --> 00:00:24.940
So in terms of special influence,

00:00:24.940 --> 00:00:27.690
only the Senate, not the
House of Representatives,

00:00:27.690 --> 00:00:30.480
is involved in ratifying treaties.

00:00:31.400 --> 00:00:33.100
The executive, the President,

00:00:33.100 --> 00:00:34.950
they can negotiate a treaty

00:00:34.950 --> 00:00:37.890
but it does not become effective binding

00:00:37.890 --> 00:00:39.790
from a United States point of view

00:00:39.790 --> 00:00:42.790
until it is ratified by
the United States Senate,

00:00:42.790 --> 00:00:47.310
and it has to be ratified
by a 2/3 super majority.

00:00:47.310 --> 00:00:49.520
This is one of the
reasons why it is viewed

00:00:49.520 --> 00:00:52.510
that the Senate has more
influence on foreign relations

00:00:52.510 --> 00:00:54.810
than the House of Representatives.

00:00:54.810 --> 00:00:56.860
The other area that the Senate is involved

00:00:56.860 --> 00:00:59.400
is in confirming appointments.

00:00:59.400 --> 00:01:02.700
These could be appointments
to the President's cabinet.

00:01:02.700 --> 00:01:04.690
These could also be
judiciary appointments.

00:01:04.690 --> 00:01:06.320
It could be to lower federal courts

00:01:06.320 --> 00:01:08.680
or to the United States Supreme Court.

00:01:08.680 --> 00:01:12.180
The House of Representatives
once again is not involved.

00:01:12.180 --> 00:01:13.940
But to appreciate just how things

00:01:13.940 --> 00:01:15.060
go through the Senate,

00:01:15.060 --> 00:01:16.490
whether we're talking about appointments

00:01:16.490 --> 00:01:19.010
or even if we're talking
about general legislation,

00:01:19.010 --> 00:01:22.600
let's remind ourselves
the overall process.

00:01:22.600 --> 00:01:25.140
So let's just say that this
is a piece of legislation,

00:01:25.140 --> 00:01:26.470
right over here.

00:01:26.470 --> 00:01:30.800
It could have been drafted
by a staffer for a senator,

00:01:30.800 --> 00:01:33.030
maybe with help from some constituents

00:01:33.030 --> 00:01:34.800
or from some special interest groups

00:01:34.800 --> 00:01:35.970
and maybe some lobbyist,

00:01:35.970 --> 00:01:40.170
and it will be introduced to
an appropriate committee by

00:01:40.170 --> 00:01:43.200
a senator or by a group of senators.

00:01:43.200 --> 00:01:44.940
For example, if this legislation

00:01:44.940 --> 00:01:46.320
is about the Armed Services,

00:01:46.320 --> 00:01:48.800
it would go to the Armed
Services Committee.

00:01:48.800 --> 00:01:51.680
The committee could decide
to have some hearings

00:01:51.680 --> 00:01:53.600
around the legislation.

00:01:53.600 --> 00:01:55.760
Maybe they bring in the
Secretary of Defense.

00:01:55.760 --> 00:01:57.730
Maybe they bring in some military leaders.

00:01:57.730 --> 00:01:59.950
And ask them questions about their views

00:01:59.950 --> 00:02:02.050
about whether the legislation
is a good idea or not,

00:02:02.050 --> 00:02:04.210
or they just want general context.

00:02:04.210 --> 00:02:07.830
Then, they might also have some debate.

00:02:07.830 --> 00:02:09.870
Then they might decide

00:02:09.870 --> 00:02:11.390
to vote

00:02:11.390 --> 00:02:13.280
on that legislation.

00:02:13.280 --> 00:02:14.610
If that vote passes,

00:02:14.610 --> 00:02:16.600
if they get a majority in that committee,

00:02:16.600 --> 00:02:19.810
then it will go to the Senate

00:02:19.810 --> 00:02:21.140
floor.

00:02:21.140 --> 00:02:23.170
Before we even talk about what happens

00:02:23.170 --> 00:02:24.770
on the floor of the Senate,

00:02:24.770 --> 00:02:27.010
because that's where things
get really interesting,

00:02:27.010 --> 00:02:29.610
it's important to point out
that even within committee,

00:02:29.610 --> 00:02:31.430
the leadership has a lot of influence

00:02:31.430 --> 00:02:33.480
and the leadership is generally controlled

00:02:33.480 --> 00:02:35.070
by the majority party.

00:02:35.070 --> 00:02:36.660
Because the leadership might decide

00:02:36.660 --> 00:02:38.970
that hey you know what, they're
not interested in this bill,

00:02:38.970 --> 00:02:41.450
so instead of going
through this process here,

00:02:41.450 --> 00:02:44.010
they might just decide to table the bill

00:02:44.010 --> 00:02:46.909
which kind of just puts it into a limbo.

00:02:46.909 --> 00:02:48.770
But let's talk about the reality

00:02:48.770 --> 00:02:50.280
where it does get voted on.

00:02:50.280 --> 00:02:54.830
It does get a majority and
it goes to the Senate floor.

00:02:54.830 --> 00:02:56.850
What's going to happen
next in the Senate floor

00:02:56.850 --> 00:02:58.560
is a debate

00:02:58.560 --> 00:03:01.470
over that bill, and I'm
writing debate in caps

00:03:01.470 --> 00:03:04.610
because the Senate is
famous for its debates.

00:03:04.610 --> 00:03:07.630
The whole idea of ending a
debate so that you can vote

00:03:07.630 --> 00:03:09.450
is critical inside of the Senate.

00:03:09.450 --> 00:03:10.380
Once you get to the vote,

00:03:10.380 --> 00:03:12.920
if we're talking about a
general piece of legislation,

00:03:12.920 --> 00:03:15.170
if we're talking about an appointment,

00:03:15.170 --> 00:03:16.970
then you just need a simple majority.

00:03:16.970 --> 00:03:21.000
So you just need 51 votes to pass.

00:03:21.000 --> 00:03:22.970
Some of you might say, hold on a second,

00:03:22.970 --> 00:03:24.620
I've always heard that at the Senate,

00:03:24.620 --> 00:03:26.640
in order to do anything,
so need a super majority.

00:03:26.640 --> 00:03:29.100
You might have heard the 60 vote number.

00:03:29.100 --> 00:03:31.730
The reason why you hear
that is because many times

00:03:31.730 --> 00:03:33.530
the folks who do not wanna have a vote

00:03:33.530 --> 00:03:34.840
especially if they think that the vote

00:03:34.840 --> 00:03:36.120
is going to go against them,

00:03:36.120 --> 00:03:38.050
that one senator or it
could be a group of senators

00:03:38.050 --> 00:03:40.180
that say, hey, I want
to keep debating on it,

00:03:40.180 --> 00:03:44.360
and this protracted debate
is known as a filibuster,

00:03:44.360 --> 00:03:46.550
which is a very strange word.

00:03:46.550 --> 00:03:49.210
It was originally in reference to pirates

00:03:49.210 --> 00:03:51.690
but it came to mean folks
who were trying to hold up

00:03:51.690 --> 00:03:53.350
to the legislation process.

00:03:53.350 --> 00:03:55.280
Its become a mechanism by which

00:03:55.280 --> 00:03:56.580
the folks who don't want the vote,

00:03:56.580 --> 00:03:58.840
who might be against the bill,
who might be in the minority,

00:03:58.840 --> 00:04:01.330
they might not have enough
votes to defeat the bill

00:04:01.330 --> 00:04:03.800
might still try to hold things up.

00:04:03.800 --> 00:04:05.850
The reason why you heard about 60 votes

00:04:05.850 --> 00:04:07.670
is because generally speaking,

00:04:07.670 --> 00:04:10.210
that is a how you stop a filibuster.

00:04:10.210 --> 00:04:12.360
If you wanna stop a filibuster,

00:04:12.360 --> 00:04:14.690
you need to do something called cloture.

00:04:14.690 --> 00:04:16.370
Or another way of thinking about it is

00:04:16.370 --> 00:04:19.760
closure of the debate so
that you can get to a vote.

00:04:19.760 --> 00:04:21.190
The reason why you hear 60 votes

00:04:21.190 --> 00:04:22.930
is for general legislation,

00:04:22.930 --> 00:04:26.820
you need 60 votes in
order to have cloture.

00:04:26.820 --> 00:04:28.440
So even though you only need 51 votes

00:04:28.440 --> 00:04:30.740
for the legislation to
pass once you vote on it,

00:04:30.740 --> 00:04:33.360
to even get to that
point, you need 60 votes.

00:04:33.360 --> 00:04:35.230
This is why you hear
that for a legislation

00:04:35.230 --> 00:04:36.900
to actually get through the Senate,

00:04:36.900 --> 00:04:38.960
you need the 60 votes.

00:04:38.960 --> 00:04:41.000
There is an exception to this.

00:04:41.000 --> 00:04:43.620
That exception is around appointments.

00:04:44.490 --> 00:04:46.790
Prior to 2013,

00:04:46.790 --> 00:04:49.510
in order to have cloture
for an appointment,

00:04:49.510 --> 00:04:51.590
you also needed 60 votes.

00:04:51.590 --> 00:04:54.080
But in 2013, it was decided that

00:04:54.080 --> 00:04:58.670
for non-Supreme Court
appointments, you only needed 51

00:04:58.670 --> 00:05:00.280
votes for

00:05:00.280 --> 00:05:01.113
cloture.

00:05:01.113 --> 00:05:04.060
Then in 2017, this was extended also

00:05:04.060 --> 00:05:06.470
to Supreme Court appointments.

00:05:06.470 --> 00:05:09.250
Now for appointments,
you only need 51 votes

00:05:09.250 --> 00:05:11.835
for a cloture to end a filibuster.

00:05:11.835 --> 00:05:14.880
And of course you only need
51 votes for the confirmation,

00:05:14.880 --> 00:05:17.500
so functionally, you just
need A simple majority now

00:05:17.500 --> 00:05:20.340
in the Senate for confirmations.

00:05:20.340 --> 00:05:22.490
But legislation, you need 60 votes.

00:05:22.490 --> 00:05:24.210
And of course for things like treaties,

00:05:24.210 --> 00:05:26.040
you need a 2/3 super majority

00:05:26.040 --> 00:05:28.810
to convict someone in an
impeachment, say the President,

00:05:28.810 --> 00:05:30.580
you need 2/3 super majority.

00:05:30.580 --> 00:05:31.820
And like the House,

00:05:31.820 --> 00:05:34.760
if we're talking about
overriding a presidential veto

00:05:34.760 --> 00:05:38.980
or amending the constitution,
you need a 2/3 majority.

00:05:38.980 --> 00:05:41.070
What I've just talked
about, it isn't extensive,

00:05:41.070 --> 00:05:44.520
it isn't exhaustive of all of
the processes in the Senate.

00:05:44.520 --> 00:05:46.770
But hopefully, it gives
you appreciation of,

00:05:46.770 --> 00:05:49.720
one, areas where the Senate
has special influence,

00:05:49.720 --> 00:05:52.800
and also how the rules and
processes of the Senate

00:05:52.800 --> 00:05:55.240
can be leveraged by
either majority parties

00:05:55.240 --> 00:05:58.230
or minority parties in
order to get things done.

00:05:58.230 --> 00:05:59.790
And how in the Senate,

00:05:59.790 --> 00:06:02.620
it is harder for a simple majority

00:06:02.620 --> 00:06:04.120
to do whatever they want.


Introduction to circuits and Ohm's law

WEBVTT
Kind: captions
Language: en

00:00:00.300 --> 00:00:02.250
- [Instructor] What we
will introduce ourselves to

00:00:02.250 --> 00:00:05.840
in this video is the
notion of electric circuits

00:00:05.840 --> 00:00:08.550
and Ohm's law, which you can view

00:00:08.550 --> 00:00:10.430
as the most fundamental law

00:00:10.430 --> 00:00:12.449
or the most basic law or simplest law

00:00:12.449 --> 00:00:14.580
when we are dealing with circuits.

00:00:14.580 --> 00:00:17.521
And it connects the ideas of voltage,

00:00:17.521 --> 00:00:20.960
which we will get more
of a intuitive idea for

00:00:20.960 --> 00:00:23.500
in a second, and current,

00:00:24.670 --> 00:00:27.560
which is denoted by capital letter I,

00:00:27.560 --> 00:00:30.380
I guess to avoid confusion
if they used a capital C

00:00:30.380 --> 00:00:32.010
with the coulomb.

00:00:32.010 --> 00:00:36.213
And what connects these two
is the notion of resistance.

00:00:36.213 --> 00:00:37.130
Resistance,

00:00:38.350 --> 00:00:41.280
that is denoted with the capital letter R.

00:00:41.280 --> 00:00:43.240
And just to cut to the chase,

00:00:43.240 --> 00:00:44.920
the relationship between these

00:00:44.920 --> 00:00:47.630
is a pretty simple mathematical one.

00:00:47.630 --> 00:00:51.797
It is that voltage is equal to current

00:00:53.080 --> 00:00:56.510
times resistance or
another way to view it,

00:00:56.510 --> 00:00:59.120
if you divide both sides by resistance,

00:00:59.120 --> 00:01:03.910
you get that current is equal to voltage

00:01:03.910 --> 00:01:05.730
divided by resistance.

00:01:05.730 --> 00:01:09.740
Voltage divided by resistance.

00:01:09.740 --> 00:01:12.270
But intuitively, what is voltage?

00:01:12.270 --> 00:01:13.630
What is current?

00:01:13.630 --> 00:01:15.590
And what is resistance?

00:01:15.590 --> 00:01:17.140
And what are the units for them

00:01:17.140 --> 00:01:19.071
so that we can make sense of this?

00:01:19.071 --> 00:01:22.100
So to get an intuition
for what these things are

00:01:22.100 --> 00:01:26.330
and how they relate, let's
build a metaphor using

00:01:26.330 --> 00:01:29.588
the flow of water, which
isn't a perfect metaphor,

00:01:29.588 --> 00:01:32.930
but it helps me at least
understand the relationship

00:01:32.930 --> 00:01:35.460
between voltage, current, and resistance.

00:01:35.460 --> 00:01:37.680
So let's say I have this
vertical pipe of water,

00:01:37.680 --> 00:01:39.400
it's closed at the bottom right now,

00:01:39.400 --> 00:01:40.750
and it's all full of water.

00:01:40.750 --> 00:01:44.510
There's water above here as well.

00:01:44.510 --> 00:01:46.379
So the water in the pipe,

00:01:46.379 --> 00:01:49.800
so let's say the water right over here,

00:01:49.800 --> 00:01:52.980
it's gonna have some potential energy.

00:01:52.980 --> 00:01:55.730
And this potential energy, as we will see,

00:01:55.730 --> 00:01:58.270
it is analogous to voltage.

00:01:58.270 --> 00:02:02.437
Voltage is electric
potential, electric potential.

00:02:04.520 --> 00:02:07.020
Now it isn't straight up potential energy,

00:02:07.020 --> 00:02:10.230
it's actually potential
energy per unit charge.

00:02:10.230 --> 00:02:11.100
So let me write that.

00:02:11.100 --> 00:02:15.270
Potential energy per unit,

00:02:15.270 --> 00:02:17.010
unit charge.

00:02:17.010 --> 00:02:20.180
You could think of it as joules,
which is potential energy,

00:02:20.180 --> 00:02:22.660
or units of energy per coulomb.

00:02:22.660 --> 00:02:24.530
That is our unit charge.

00:02:24.530 --> 00:02:28.697
And the units for voltage
in general is volts.

00:02:30.250 --> 00:02:32.160
Now, let's think about what would happen

00:02:32.160 --> 00:02:35.070
if we now open the bottom of this pipe.

00:02:35.070 --> 00:02:37.730
So we open this up.

00:02:37.730 --> 00:02:38.563
What's gonna happen?

00:02:38.563 --> 00:02:42.220
Well, the water's immediately
gonna drop straight down.

00:02:42.220 --> 00:02:44.300
That potential energy
is gonna be converted

00:02:44.300 --> 00:02:45.850
to kinetic energy.

00:02:45.850 --> 00:02:48.410
And you could look at a
certain part of the pipe

00:02:48.410 --> 00:02:49.910
right over here, right over here.

00:02:49.910 --> 00:02:50.743
And you could say, well,

00:02:50.743 --> 00:02:54.867
how much water is flowing per unit time?

00:02:55.740 --> 00:02:58.480
And that amount of water that is flowing

00:02:58.480 --> 00:03:00.150
through the pipe at that point

00:03:00.150 --> 00:03:01.950
in a specific amount of time,

00:03:01.950 --> 00:03:05.280
that is analogous to current.

00:03:05.280 --> 00:03:08.330
Current is the amount of charge,

00:03:08.330 --> 00:03:11.060
so we could say charge per unit time.

00:03:11.060 --> 00:03:12.800
Q for charge,

00:03:14.130 --> 00:03:16.900
and t for time.

00:03:16.900 --> 00:03:18.320
And intuitively you could say,

00:03:18.320 --> 00:03:22.487
how much, how much charge

00:03:23.750 --> 00:03:24.780
flowing,

00:03:25.860 --> 00:03:27.420
flowing past

00:03:28.620 --> 00:03:33.290
a point in a circuit, a point in

00:03:33.290 --> 00:03:34.123
circuit

00:03:35.810 --> 00:03:38.780
in a, let's say, unit of time,

00:03:38.780 --> 00:03:41.460
we could think of it as a second.

00:03:41.460 --> 00:03:44.670
And so you could also think
about it as coulombs per second,

00:03:44.670 --> 00:03:46.990
charge per unit time.

00:03:46.990 --> 00:03:49.870
And the idea of resistance
is something could just keep

00:03:49.870 --> 00:03:54.440
that charge from flowing at
an arbitrarily high rate.

00:03:54.440 --> 00:03:57.070
And if we want to go back
to our water metaphor,

00:03:57.070 --> 00:04:00.080
what we could do is, we
could introduce something

00:04:00.080 --> 00:04:02.180
that would impede the water,

00:04:02.180 --> 00:04:05.320
and that could be a narrowing of the pipe.

00:04:05.320 --> 00:04:07.850
And that narrowing of the pipe

00:04:07.850 --> 00:04:10.490
would be analogous to resistance.

00:04:11.410 --> 00:04:13.230
So in this situation, once again,

00:04:13.230 --> 00:04:14.690
I have my vertical water pipe,

00:04:14.690 --> 00:04:15.880
I have opened it up,

00:04:15.880 --> 00:04:18.040
and you still would have
that potential energy,

00:04:18.040 --> 00:04:19.690
which is analogous to voltage,

00:04:19.690 --> 00:04:22.380
and it would be converted
to kinetic energy,

00:04:22.380 --> 00:04:26.250
and you would have a flow
of water through that pipe,

00:04:26.250 --> 00:04:29.040
but now at every point in this pipe,

00:04:29.040 --> 00:04:31.400
the amount of water that's flowing past

00:04:31.400 --> 00:04:33.890
at a given moment of
time is gonna be lower,

00:04:33.890 --> 00:04:37.840
because you have literally this
bottleneck right over here.

00:04:37.840 --> 00:04:41.840
So this narrowing is
analogous to resistance.

00:04:41.840 --> 00:04:43.280
How

00:04:43.280 --> 00:04:44.840
much

00:04:44.840 --> 00:04:45.840
charge

00:04:46.850 --> 00:04:47.810
flow

00:04:48.960 --> 00:04:49.850
impeded,

00:04:51.220 --> 00:04:52.170
impeded.

00:04:52.170 --> 00:04:55.520
And the unit here is the ohm,

00:04:55.520 --> 00:04:57.000
is the ohm,

00:04:57.000 --> 00:05:01.560
which is denoted with
the Greek letter omega.

00:05:01.560 --> 00:05:03.450
So now that we've defined these things

00:05:03.450 --> 00:05:04.710
and we have our metaphor,

00:05:04.710 --> 00:05:07.290
let's actually look at
an electric circuit.

00:05:07.290 --> 00:05:10.620
So first, let me construct a battery.

00:05:10.620 --> 00:05:13.800
So this is my battery.

00:05:13.800 --> 00:05:17.380
And the convention is my negative terminal

00:05:17.380 --> 00:05:18.700
is the shorter line here.

00:05:18.700 --> 00:05:20.220
So I could say that's
the negative terminal,

00:05:20.220 --> 00:05:22.390
that is the positive terminal.

00:05:22.390 --> 00:05:24.280
Associated with that battery,

00:05:24.280 --> 00:05:26.020
I could have some voltage.

00:05:26.020 --> 00:05:27.910
And just to make this tangible,

00:05:27.910 --> 00:05:29.470
let's say the voltage

00:05:30.610 --> 00:05:34.720
is equal to 16 volts across this battery.

00:05:34.720 --> 00:05:36.650
And so one way to think about it is

00:05:36.650 --> 00:05:39.300
the potential energy per unit charge,

00:05:39.300 --> 00:05:40.760
let's say we have electrons here

00:05:40.760 --> 00:05:42.620
at the negative terminal,

00:05:42.620 --> 00:05:46.900
the potential energy per
coulomb here is 16 volts.

00:05:46.900 --> 00:05:49.400
These electrons, if they have a path,

00:05:49.400 --> 00:05:52.120
would go to the positive terminal.

00:05:52.120 --> 00:05:54.992
And so we can provide a path.

00:05:54.992 --> 00:05:56.920
Let me draw it like this.

00:05:56.920 --> 00:05:59.470
At first, I'm gonna not
make the path available

00:05:59.470 --> 00:06:03.630
to the electrons, I'm gonna
have an open circuit here.

00:06:03.630 --> 00:06:06.380
I'm gonna make this path

00:06:06.380 --> 00:06:07.380
for the electrons.

00:06:07.380 --> 00:06:11.370
And so as long as our
circuit is open like this,

00:06:11.370 --> 00:06:14.150
this is actually analogous
to the closed pipe.

00:06:14.150 --> 00:06:16.440
The electrons, there is
no way for them to get

00:06:16.440 --> 00:06:18.300
to the positive terminal.

00:06:18.300 --> 00:06:21.142
But if we were to close the
circuit right over here,

00:06:21.142 --> 00:06:23.940
if we were to close it,
then all of a sudden,

00:06:23.940 --> 00:06:28.660
the electrons could begin
to flow through this circuit

00:06:28.660 --> 00:06:30.510
in an analogous way to the way

00:06:30.510 --> 00:06:33.237
that the water would flow down this pipe.

00:06:33.237 --> 00:06:35.900
Now when you see a
schematic diagram like this,

00:06:35.900 --> 00:06:37.400
when you just see these lines,

00:06:37.400 --> 00:06:40.325
those usually denote something
that has no resistance.

00:06:40.325 --> 00:06:42.090
But that's very theoretical.

00:06:42.090 --> 00:06:45.670
In practice, even a very simple
wire that's a good conductor

00:06:45.670 --> 00:06:47.640
would have some resistance.

00:06:47.640 --> 00:06:52.545
And the way that we denote
resistance is with a jagged line.

00:06:52.545 --> 00:06:55.990
And so let me draw resistance here.

00:06:55.990 --> 00:06:58.910
So that is how we denote
it in a circuit diagram.

00:06:58.910 --> 00:07:02.210
Now let's say the resistance
here is eight ohms.

00:07:03.450 --> 00:07:05.320
So my question to you is,

00:07:05.320 --> 00:07:07.860
given the voltage and
given the resistance,

00:07:07.860 --> 00:07:11.230
what will be the current
through this circuit?

00:07:11.230 --> 00:07:14.170
What is the rate at which
charge will flow past

00:07:14.170 --> 00:07:16.540
a point in this circuit?

00:07:16.540 --> 00:07:18.892
Pause this video and try to figure it out.

00:07:18.892 --> 00:07:21.160
Well, to answer that question,

00:07:21.160 --> 00:07:23.400
you just have to go to Ohm's law.

00:07:23.400 --> 00:07:25.990
We wanna solve for current,
we know the voltage,

00:07:25.990 --> 00:07:27.570
we know the resistance.

00:07:27.570 --> 00:07:31.770
So the current in this example
is going to be our voltage

00:07:31.770 --> 00:07:36.230
which is 16 volts,
divided by our resistance

00:07:36.230 --> 00:07:37.850
which is eight ohms.

00:07:38.850 --> 00:07:41.510
And so this is going to be 16 divided

00:07:41.510 --> 00:07:44.470
by eight is equal to two

00:07:44.470 --> 00:07:47.600
and the units for our current,

00:07:47.600 --> 00:07:51.080
which is charge per unit
time, coulombs per second,

00:07:51.080 --> 00:07:53.140
you could say two coulombs per second,

00:07:53.140 --> 00:07:55.660
or you could say amperes.

00:07:55.660 --> 00:07:59.000
And we can denote
amperes with a capital A.

00:07:59.000 --> 00:08:01.260
We talked about these electrons flowing,

00:08:01.260 --> 00:08:03.710
and you're gonna have two coulombs worth

00:08:03.710 --> 00:08:05.650
of electrons flowing per second

00:08:05.650 --> 00:08:08.440
past any point on this circuit.

00:08:08.440 --> 00:08:09.900
And it's true at any point,

00:08:09.900 --> 00:08:12.270
same reason that we saw over here.

00:08:12.270 --> 00:08:14.985
Even though it's wider up
here and it's narrower here,

00:08:14.985 --> 00:08:18.010
because of this bottleneck,
the same amount of water

00:08:18.010 --> 00:08:20.590
that flows through this
part of the pipe in a second

00:08:20.590 --> 00:08:22.650
would have to be the same
amount that flows through

00:08:22.650 --> 00:08:24.620
that part of the pipe in a second.

00:08:24.620 --> 00:08:26.760
And that's why for this circuit,

00:08:26.760 --> 00:08:28.540
for this very simple circuit,

00:08:28.540 --> 00:08:30.600
the current that you would
measure at that point,

00:08:30.600 --> 00:08:32.853
this point, and this point,
would all be the same.

00:08:32.853 --> 00:08:34.582
But there is a quirk.

00:08:34.582 --> 00:08:36.830
Pause this video and think
about what do you think

00:08:36.830 --> 00:08:38.780
would be the direction for the current?

00:08:39.640 --> 00:08:41.410
Well, if you knew about electrons

00:08:41.410 --> 00:08:42.340
and what was going on,

00:08:42.340 --> 00:08:44.250
you would say, well, the
electrons are flowing

00:08:44.250 --> 00:08:45.580
in this direction.

00:08:45.580 --> 00:08:47.490
And so for this electric current,

00:08:47.490 --> 00:08:49.372
I would say that it was flowing in,

00:08:49.372 --> 00:08:52.970
I would denote the
current going like that.

00:08:52.970 --> 00:08:55.340
Well, it turns out that
the convention we use

00:08:55.340 --> 00:08:56.930
is the opposite of that.

00:08:56.930 --> 00:08:59.580
And that's really a historical quirk.

00:08:59.580 --> 00:09:02.756
When Benjamin Franklin was
first studying circuits,

00:09:02.756 --> 00:09:05.540
he did not know about electrons.

00:09:05.540 --> 00:09:08.940
They would be discovered
roughly 150 years later.

00:09:08.940 --> 00:09:12.390
He just knew that what he
was labeling as charge,

00:09:12.390 --> 00:09:14.710
and he arbitrarily labeled
positive and negative,

00:09:14.710 --> 00:09:16.020
he just knew they were opposites,

00:09:16.020 --> 00:09:18.800
he knew something like charge was flowing.

00:09:18.800 --> 00:09:22.660
And so, in his studies of electricity,

00:09:22.660 --> 00:09:25.220
he denoted current as going

00:09:25.220 --> 00:09:28.770
from the positive to
the negative terminal.

00:09:28.770 --> 00:09:31.460
And so we still use that convention today,

00:09:31.460 --> 00:09:33.420
even though that is the
opposite of the direction

00:09:33.420 --> 00:09:34.750
of the flow of electrons.

00:09:34.750 --> 00:09:36.520
And as we will see later on,

00:09:36.520 --> 00:09:39.511
current doesn't always involve electrons.

00:09:39.511 --> 00:09:42.130
And so this current here is going to be

00:09:42.130 --> 00:09:45.220
a two ampere current.


How to recognize relative and absolute maxima and minima

WEBVTT
Kind: captions
Language: en

00:00:00.450 --> 00:00:02.006
- [Instructor] We're asked to mark all

00:00:02.006 --> 00:00:06.006
the relative extremum
points in the graph below.

00:00:06.859 --> 00:00:09.343
So pause the video and see
if you can have a go at that,

00:00:09.343 --> 00:00:11.665
just try to maybe look at the screen and,

00:00:11.665 --> 00:00:15.218
in your head see if you can
identify the relative extrema.

00:00:15.218 --> 00:00:16.983
So now let's do this together.

00:00:16.983 --> 00:00:18.956
So there's two types of relative extrema.

00:00:18.956 --> 00:00:22.347
You have your relative maximum points,

00:00:22.347 --> 00:00:25.847
and you have your relative minimum points.

00:00:27.455 --> 00:00:29.777
And a relative maximum
point or relative minimum,

00:00:29.777 --> 00:00:33.167
they're relatively easy
(laughing) to spot out visually.

00:00:33.167 --> 00:00:35.953
You will see a relative maximum point as

00:00:35.953 --> 00:00:37.602
the high point on a hill,

00:00:37.602 --> 00:00:39.227
and the hill itself
doesn't even have to be

00:00:39.227 --> 00:00:40.226
the highest hill.

00:00:40.226 --> 00:00:42.200
For example the curve
could go at other parts

00:00:42.200 --> 00:00:44.080
of the domain of the function,

00:00:44.080 --> 00:00:46.077
could go to higher values.

00:00:46.077 --> 00:00:48.469
It could also look like
the peak of a mountain,

00:00:48.469 --> 00:00:50.025
and once again since we're talking about

00:00:50.025 --> 00:00:51.348
the relative maximum,

00:00:51.348 --> 00:00:52.765
this mountain peak doesn't
have to be the highest

00:00:52.765 --> 00:00:53.763
mountain peak.

00:00:53.763 --> 00:00:56.039
There could be higher mountains,

00:00:56.039 --> 00:00:57.920
and actually each of these peaks,

00:00:57.920 --> 00:01:01.124
each of these peaks would
be a relative maximum point.

00:01:01.124 --> 00:01:03.701
Now relative minima are the opposite.

00:01:03.701 --> 00:01:07.486
They would be the bottom of your valleys.

00:01:07.486 --> 00:01:09.855
So that's a relative minimum point.

00:01:09.855 --> 00:01:12.780
This right over here is
a relative minimum point,

00:01:12.780 --> 00:01:14.591
even if there are other
parts of the function

00:01:14.591 --> 00:01:16.542
that are lower.

00:01:16.542 --> 00:01:18.980
Now there's also an edge
case for both relative

00:01:18.980 --> 00:01:21.209
maxima and relative minima,

00:01:21.209 --> 00:01:24.808
and that's where the graph is flat.

00:01:24.808 --> 00:01:27.200
So if you have parts
of your function where

00:01:27.200 --> 00:01:28.709
it's just constant,

00:01:28.709 --> 00:01:30.660
these points would actually be both.

00:01:30.660 --> 00:01:33.493
For example, if this is our x-axis

00:01:34.700 --> 00:01:36.720
right over here,

00:01:36.720 --> 00:01:38.090
that's our x-axis,

00:01:38.090 --> 00:01:41.248
if this is our y-axis right over there,

00:01:41.248 --> 00:01:43.872
and if this is x equals c,

00:01:43.872 --> 00:01:47.099
if you construct an
open interval around c,

00:01:47.099 --> 00:01:50.536
you notice that the value
of our function at c,

00:01:50.536 --> 00:01:53.508
f of c, is at least as large as the values

00:01:53.508 --> 00:01:55.760
of the function around it.

00:01:55.760 --> 00:01:57.572
And it is also at least as small

00:01:57.572 --> 00:01:59.801
as the values of the function around it,

00:01:59.801 --> 00:02:01.356
so this point would also be considered

00:02:01.356 --> 00:02:03.980
a relative minimum point.

00:02:03.980 --> 00:02:07.579
But that's an edge case that
you won't encounter as often.

00:02:07.579 --> 00:02:08.880
So with that primer out of the way,

00:02:08.880 --> 00:02:11.666
let's identify the relative extrema.

00:02:11.666 --> 00:02:14.615
So first the relative maximum points.

00:02:14.615 --> 00:02:17.355
Well that's a top of a
hill right over there,

00:02:17.355 --> 00:02:18.980
this is the top of a hill.

00:02:18.980 --> 00:02:20.861
You might be tempted to look
at that point and that point,

00:02:20.861 --> 00:02:22.742
but notice, at this point right over here,

00:02:22.742 --> 00:02:23.973
if you go to the right,

00:02:23.973 --> 00:02:25.807
you have values that are higher than it.

00:02:25.807 --> 00:02:27.827
So it's really not at the top of a hill.

00:02:27.827 --> 00:02:29.545
And right over if you go to the left,

00:02:29.545 --> 00:02:31.473
you have values that are higher than it,

00:02:31.473 --> 00:02:34.770
so it's also not the top of a hill.

00:02:34.770 --> 00:02:36.883
And what about the
relative minimum points?

00:02:36.883 --> 00:02:41.690
Well this one right over here
is a relative minimum point.

00:02:41.690 --> 00:02:46.357
This one right over here is
a relative minimum point.

00:02:46.357 --> 00:02:48.098
And this one over here

00:02:48.098 --> 00:02:50.420
is a relative minimum point.

00:02:50.420 --> 00:02:54.971
Now let's do an example
dealing with absolute extrema.

00:02:54.971 --> 00:02:58.756
So here we're told to
mark the absolute maximum

00:02:58.756 --> 00:03:01.032
and the absolute minimum points

00:03:01.032 --> 00:03:03.214
in the graph below.

00:03:03.214 --> 00:03:04.213
So once again,

00:03:04.213 --> 00:03:07.649
pause this video and see if
you can have a go at this.

00:03:07.649 --> 00:03:10.732
So you have an absolute maximum point

00:03:12.386 --> 00:03:14.553
at let's say x equals c

00:03:15.637 --> 00:03:19.074
if and only if, so I'll write iff

00:03:19.074 --> 00:03:21.233
for if and only if,

00:03:21.233 --> 00:03:24.066
f of c is greater than or equal to

00:03:25.041 --> 00:03:29.208
f of x for all the x's in
the domain of the function.

00:03:30.196 --> 00:03:32.863
And you have an absolute minimum

00:03:33.888 --> 00:03:35.221
at x equals c

00:03:36.187 --> 00:03:37.854
if and only if, iff,

00:03:39.252 --> 00:03:41.835
f of c is less than or equal to

00:03:42.828 --> 00:03:46.125
f of x for all the x's over the domain.

00:03:46.125 --> 00:03:48.099
So another way to think about it is,

00:03:48.099 --> 00:03:51.419
absolute maximum point is the high point.

00:03:51.419 --> 00:03:55.134
So over here, that is the
absolute maximum point.

00:03:55.134 --> 00:03:57.340
And then the absolute
minimum point is interesting

00:03:57.340 --> 00:03:58.548
because in this case,

00:03:58.548 --> 00:03:59.987
it would be actually one of,

00:03:59.987 --> 00:04:02.286
it would happen at one of
the endpoints of our domain.

00:04:02.286 --> 00:04:04.619
So that is our absolute max,

00:04:06.884 --> 00:04:10.390
and this right over here is our absolute,

00:04:10.390 --> 00:04:11.473
absolute min.

00:04:12.480 --> 00:04:14.267
Now once again there is an edge case

00:04:14.267 --> 00:04:16.195
that you will not see too frequently.

00:04:16.195 --> 00:04:17.495
So for example,

00:04:17.495 --> 00:04:19.562
if this function did something like this,

00:04:19.562 --> 00:04:22.116
so if it went up like this,

00:04:22.116 --> 00:04:25.366
and then it just stayed flat like this,

00:04:26.249 --> 00:04:28.269
then this would no longer be an absolute

00:04:28.269 --> 00:04:29.569
maximum point.

00:04:29.569 --> 00:04:32.797
But any of these points
in this flat region,

00:04:32.797 --> 00:04:35.839
because they are at least
as high as any other points

00:04:35.839 --> 00:04:37.487
on our entire curve,

00:04:37.487 --> 00:04:42.039
any of those could be considered
absolute maximum points.

00:04:42.039 --> 00:04:44.686
But we aren't dealing with
that edge case in this example,

00:04:44.686 --> 00:04:46.427
and you're less likely to see that.

00:04:46.427 --> 00:04:48.145
And so in most problems,

00:04:48.145 --> 00:04:49.446
it's pretty easy to pick out.

00:04:49.446 --> 00:04:51.744
Because the absolute
highest point on the curve

00:04:51.744 --> 00:04:53.765
will often be your absolute maximum,

00:04:53.765 --> 00:04:55.831
and the absolute lowest
point on your curve

00:04:55.831 --> 00:04:57.466
will be your absolute minimum.


Arteries vs. veins-what's the difference?

WEBVTT
Kind: captions
Language: en

00:00:00.933 --> 00:00:02.038
- [Instructor] Let's talk a little bit

00:00:02.038 --> 00:00:04.769
about arteries and veins
and the roles they play

00:00:04.769 --> 00:00:07.091
in the circulatory system.

00:00:07.091 --> 00:00:08.647
So I want you to pause this video

00:00:08.647 --> 00:00:09.784
and first think to yourself,

00:00:09.784 --> 00:00:12.977
Do you have a sense of what
arteries and veins are?

00:00:12.977 --> 00:00:16.449
Well one idea behind arteries and veins

00:00:16.449 --> 00:00:19.432
are that well, in most of these drawings,

00:00:19.432 --> 00:00:21.313
arteries are drawn in red,

00:00:21.313 --> 00:00:24.320
and I even made the
artery word here in red.

00:00:24.320 --> 00:00:26.433
And veins are drawn in blue.

00:00:26.433 --> 00:00:29.522
And so maybe that represents
how much oxygen they have.

00:00:29.522 --> 00:00:32.610
And so one possible explanation is that

00:00:32.610 --> 00:00:35.219
arteries carry oxygenated blood,

00:00:35.219 --> 00:00:37.636
oxygenated, oxygenated blood,

00:00:40.709 --> 00:00:43.792
while veins carry deoxygenated blood.

00:00:44.867 --> 00:00:47.700
So blood that has less oxygen now.

00:00:48.690 --> 00:00:51.286
Now this is actually incorrect.

00:00:51.286 --> 00:00:53.508
It is, many times, the case that arteries

00:00:53.508 --> 00:00:55.732
are the ones carrying oxygenated blood

00:00:55.732 --> 00:00:58.323
and veins are carrying
the deoxygenated blood.

00:00:58.323 --> 00:01:01.158
But as we will see, this
is not always the case.

00:01:01.158 --> 00:01:03.666
And since we're already
talking about oxygenated blood

00:01:03.666 --> 00:01:06.256
and deoxygenated blood and
the colors red and blue,

00:01:06.256 --> 00:01:08.926
it's worth addressing
another misconception.

00:01:08.926 --> 00:01:13.651
Many times it is said that
deoxygenated blood looks blue,

00:01:13.651 --> 00:01:15.540
and the reason why people believe that

00:01:15.540 --> 00:01:18.144
is if you look at your
wrist and you're able to see

00:01:18.144 --> 00:01:19.719
some of the vessels in there,

00:01:19.719 --> 00:01:21.465
you will see some blue vessels.

00:01:21.465 --> 00:01:23.411
And those, or at least they look blue

00:01:23.411 --> 00:01:25.303
when you're looking from
the outside of your skin.

00:01:25.303 --> 00:01:27.427
And those, indeed, are veins.

00:01:27.427 --> 00:01:29.972
And so that's where the
misconception has come from,

00:01:29.972 --> 00:01:32.355
that veins, which, in your arm,

00:01:32.355 --> 00:01:34.096
are carrying deoxygenated blood.

00:01:34.096 --> 00:01:36.451
That that deoxygenated blood is blue.

00:01:36.451 --> 00:01:38.102
It turns out that it is not blue.

00:01:38.102 --> 00:01:40.131
It is just a deeper red.

00:01:40.131 --> 00:01:41.863
And the reason why the veins look blue

00:01:41.863 --> 00:01:45.904
is because of the optics of
light going through your skin

00:01:45.904 --> 00:01:48.003
and then seeing the outside of the veins

00:01:48.003 --> 00:01:49.619
and then reflecting back.

00:01:49.619 --> 00:01:51.716
That is not the color of the actual blood.

00:01:51.716 --> 00:01:54.434
So so far I have not given
you a clear definition

00:01:54.434 --> 00:01:56.548
of what arteries versus veins are.

00:01:56.548 --> 00:01:59.603
A better definition, so
let me cross these two out,

00:01:59.603 --> 00:02:03.317
are that arteries carry
blood away from the heart.

00:02:03.317 --> 00:02:04.984
Away from the heart.

00:02:08.032 --> 00:02:11.365
And veins carry blood towards the heart.

00:02:12.595 --> 00:02:14.095
Towards the heart.

00:02:15.846 --> 00:02:19.120
And I can get a zoomed in
image of the heart right here

00:02:19.120 --> 00:02:21.603
and that will make it
a little bit clearer.

00:02:21.603 --> 00:02:23.912
And you can also see,
or we're about to see,

00:02:23.912 --> 00:02:26.608
why this first definition,
or this first distinction

00:02:26.608 --> 00:02:29.522
between arteries and veins
does not always hold.

00:02:29.522 --> 00:02:32.274
So let's just imagine
some blood that is being

00:02:32.274 --> 00:02:34.869
pumped away from the heart.

00:02:34.869 --> 00:02:37.331
So right when it gets
pumped away from the heart,

00:02:37.331 --> 00:02:38.643
it'll be right over here.

00:02:38.643 --> 00:02:40.529
It gets pumped through the aorta,

00:02:40.529 --> 00:02:41.940
and you can see the aorta branches,

00:02:41.940 --> 00:02:45.622
so some blood can go up towards your head,

00:02:45.622 --> 00:02:48.516
and if it didn't, you
would pass out and die.

00:02:48.516 --> 00:02:50.489
And then a lot of the blood goes down

00:02:50.489 --> 00:02:52.774
towards the rest of your body.

00:02:52.774 --> 00:02:56.836
And that, indeed, is the
most oxygenated blood.

00:02:56.836 --> 00:02:59.429
And so it'll flow through your body.

00:02:59.429 --> 00:03:03.224
And these arteries will
keep branching and branching

00:03:03.224 --> 00:03:05.139
into smaller vessels,

00:03:05.139 --> 00:03:08.416
all the way until they form
these very small branches.

00:03:08.416 --> 00:03:10.819
And it's that place, especially,

00:03:10.819 --> 00:03:12.839
where they will lose a lot of their oxygen

00:03:12.839 --> 00:03:15.521
to the fluid and the cells around them.

00:03:15.521 --> 00:03:18.035
And then the blood is less oxygenated.

00:03:18.035 --> 00:03:20.978
And then even though
deoxygenated blood is not blue,

00:03:20.978 --> 00:03:23.656
it often gets depicted as
blue in a lot of diagrams.

00:03:23.656 --> 00:03:25.908
So I will do the same.

00:03:25.908 --> 00:03:29.991
And these vessels start
building into your veins.

00:03:32.355 --> 00:03:34.755
And these really small
vessels that really bridge

00:03:34.755 --> 00:03:36.384
between arteries and veins,

00:03:36.384 --> 00:03:39.124
where a lot of the gas and
nutrient exchange occurs,

00:03:39.124 --> 00:03:41.910
these are called capillaries.

00:03:41.910 --> 00:03:45.138
And so after going
through the capillaries,

00:03:45.138 --> 00:03:48.387
the blood will then come back to the heart

00:03:48.387 --> 00:03:51.892
and now it's coming towards
the heart through the veins.

00:03:51.892 --> 00:03:54.740
It comes into the right atrium,
then the right ventricle.

00:03:54.740 --> 00:03:57.921
Then that gets pumped towards the lungs.

00:03:57.921 --> 00:04:00.463
And this is the exception
to the first incorrect

00:04:00.463 --> 00:04:03.654
definition of arteries and
veins that we looked at.

00:04:03.654 --> 00:04:06.117
This right over here, is an artery.

00:04:06.117 --> 00:04:08.414
Even though it's carrying less oxygenated

00:04:08.414 --> 00:04:10.158
or deoxygenated blood,

00:04:10.158 --> 00:04:12.193
it's an artery because it's carrying blood

00:04:12.193 --> 00:04:13.746
away from the heart.

00:04:13.746 --> 00:04:16.001
But in this case, it's not carrying it to

00:04:16.001 --> 00:04:17.331
the rest of the body,

00:04:17.331 --> 00:04:19.345
it is carrying it to the lungs.

00:04:19.345 --> 00:04:23.178
That is why it is called
the pulmonary artery,

00:04:24.918 --> 00:04:28.467
even though it's carrying
less oxygenated blood.

00:04:28.467 --> 00:04:30.978
So that it goes to the lungs and then,

00:04:30.978 --> 00:04:35.030
in the lungs, there's more
gas exchange that occurs.

00:04:35.030 --> 00:04:38.068
The blood gets oxygenated
and then it comes back

00:04:38.068 --> 00:04:39.715
to the heart.

00:04:39.715 --> 00:04:43.395
And so it comes back to
the heart in these vessels

00:04:43.395 --> 00:04:45.294
right over here,

00:04:45.294 --> 00:04:47.522
and that even though these are carrying

00:04:47.522 --> 00:04:49.182
highly oxygenated blood,

00:04:49.182 --> 00:04:51.524
these are considered veins
because they're carrying blood

00:04:51.524 --> 00:04:53.253
towards the heart.

00:04:53.253 --> 00:04:55.670
So these are pulmonary veins.

00:04:58.500 --> 00:05:00.386
And then the cycle starts again.

00:05:00.386 --> 00:05:02.819
The pulmonary veins bring
the oxygenated blood

00:05:02.819 --> 00:05:04.886
into the left atrium
and the left ventricle,

00:05:04.886 --> 00:05:07.779
and then that pumps it
to the rest of the body

00:05:07.779 --> 00:05:11.381
to the aorta, for your
systemic circulation.

00:05:11.381 --> 00:05:12.948
You have your pulmonary circulation,

00:05:12.948 --> 00:05:17.209
which circulates the blood to,
through and from the lungs.

00:05:17.209 --> 00:05:18.656
And you have your systemic circulation,

00:05:18.656 --> 00:05:23.104
which takes the blood to and
from the rest of the body.

00:05:23.104 --> 00:05:25.533
So now that we have this main distinction

00:05:25.533 --> 00:05:27.193
between arteries and veins,

00:05:27.193 --> 00:05:28.923
what are some other interesting things

00:05:28.923 --> 00:05:30.653
that we know about it?

00:05:30.653 --> 00:05:32.960
Well one thing to keep in mind is that

00:05:32.960 --> 00:05:36.060
since arteries are being
pumped directly by the heart

00:05:36.060 --> 00:05:39.405
towards the rest of the body,
they have high pressure.

00:05:39.405 --> 00:05:42.014
I'll write that in caps.

00:05:42.014 --> 00:05:43.181
High pressure.

00:05:45.485 --> 00:05:47.325
And so if you were to have
an accident of some type,

00:05:47.325 --> 00:05:48.985
which you do not want to have,

00:05:48.985 --> 00:05:50.936
and you were to
accidentally cut an artery,

00:05:50.936 --> 00:05:52.747
because of that high pressure,

00:05:52.747 --> 00:05:55.742
it would actually spurt blood,

00:05:55.742 --> 00:05:57.705
a lot more than if you were to cut a vein.

00:05:57.705 --> 00:05:59.341
And most of the times where you get a cut,

00:05:59.341 --> 00:06:01.581
you're really just cutting capillaries.

00:06:01.581 --> 00:06:03.533
Like if you were to prick your finger,

00:06:03.533 --> 00:06:05.577
it's usually a series of
capillaries that get cut,

00:06:05.577 --> 00:06:08.381
and that's why the blood would
come out very very slowly.

00:06:08.381 --> 00:06:11.853
Now if arteries are high
pressure, veins are low pressure.

00:06:11.853 --> 00:06:13.353
Low, low pressure.

00:06:16.416 --> 00:06:17.915
And one way to think about it is

00:06:17.915 --> 00:06:20.155
the arteries, the blood
is being pumped directly

00:06:20.155 --> 00:06:21.280
by the heart.

00:06:21.280 --> 00:06:22.939
But then once it goes
through the capillaries

00:06:22.939 --> 00:06:24.508
and comes back through the veins,

00:06:24.508 --> 00:06:28.027
it's kind of sluggishly making
its way back to the heart.

00:06:28.027 --> 00:06:30.188
It's not being directly pumped.

00:06:30.188 --> 00:06:32.891
And that's why in veins,
because you don't have that

00:06:32.891 --> 00:06:35.309
high pressure to bring
everything back to the heart,

00:06:35.309 --> 00:06:38.443
you have these valves that make
sure that for the most part,

00:06:38.443 --> 00:06:41.644
the blood is going in one direction.

00:06:41.644 --> 00:06:44.284
I'm going to draw the
blood in red in the veins,

00:06:44.284 --> 00:06:46.838
just so we don't keep going
with that misconception,

00:06:46.838 --> 00:06:50.363
that blood in the veins is blue somehow.

00:06:50.363 --> 00:06:52.202
Now related to the fact that
the blood in the arteries

00:06:52.202 --> 00:06:54.535
is under higher pressure,

00:06:54.535 --> 00:06:57.113
in order to transport
a fixed volume of blood

00:06:57.113 --> 00:06:59.211
in a certain amount of
time, you need less volume.

00:06:59.211 --> 00:07:02.711
And so that's why arteries are low volume.

00:07:03.900 --> 00:07:08.428
And on the other hand,
veins are high volume.

00:07:08.428 --> 00:07:10.459
And to appreciate the difference,

00:07:10.459 --> 00:07:13.419
the blood volume in arteries
are only approximately

00:07:13.419 --> 00:07:17.059
15% of the entire blood
volume in your body,

00:07:17.059 --> 00:07:21.226
while the blood volume in
veins are closer to 65%,

00:07:22.782 --> 00:07:25.418
approximately 65%.

00:07:25.418 --> 00:07:27.241
And if you're wondering where
the rest of the blood is,

00:07:27.241 --> 00:07:29.419
about five percent is in capillaries,

00:07:29.419 --> 00:07:31.729
five percent is in your heart,

00:07:31.729 --> 00:07:33.928
and about 10% is in your lungs.

00:07:33.928 --> 00:07:35.913
So I will leave you there.

00:07:35.913 --> 00:07:38.092
The big take away:
arteries are the vessels

00:07:38.092 --> 00:07:40.824
that take blood away from the heart.

00:07:40.824 --> 00:07:43.559
Veins are the vessels that
take blood towards the heart.


Relative maxima and minima worked example

WEBVTT
Kind: captions
Language: en

00:00:00.387 --> 00:00:02.135
- [Instructor] This is
the Khan Academy exercise

00:00:02.135 --> 00:00:05.136
on relative maxima and minima,

00:00:05.136 --> 00:00:09.734
and they ask us to mark all
the relative maximum points

00:00:09.734 --> 00:00:11.464
in the graph.

00:00:11.464 --> 00:00:13.770
Like always, pause this video
and see if you can figure out

00:00:13.770 --> 00:00:16.521
which are the relative maximum points.

00:00:16.521 --> 00:00:18.364
Okay, now let's work
through this together.

00:00:18.364 --> 00:00:21.248
And just as a review, a
relative maximum point

00:00:21.248 --> 00:00:23.212
is a point of the graph

00:00:23.212 --> 00:00:27.275
where the values of the
graph around it are going

00:00:27.275 --> 00:00:29.630
to be less than or equal to the value

00:00:29.630 --> 00:00:31.848
of the graph at that point.

00:00:31.848 --> 00:00:33.849
So, for example, this
point right over here

00:00:33.849 --> 00:00:36.890
would not be a relative maximum point,

00:00:36.890 --> 00:00:38.320
because if we were to
go to the right of it,

00:00:38.320 --> 00:00:40.472
the function is larger than at this point.

00:00:40.472 --> 00:00:43.022
It has a higher value than at this point.

00:00:43.022 --> 00:00:46.016
This point over here, which
looks like a peak of a mountain,

00:00:46.016 --> 00:00:47.498
and that's a pretty good giveaway

00:00:47.498 --> 00:00:49.898
if it looks like the top of a
hill or a peak of a mountain

00:00:49.898 --> 00:00:52.439
for a form of relative maximum point.

00:00:52.439 --> 00:00:54.305
This looks like a really good candidate.

00:00:54.305 --> 00:00:56.674
If we move to the right a little bit,

00:00:56.674 --> 00:00:58.428
we get lower values for our function,

00:00:58.428 --> 00:00:59.972
and if we move to the left a little bit,

00:00:59.972 --> 00:01:01.685
we get lower values for our function,

00:01:01.685 --> 00:01:04.027
and so this is a relative maximum point.

00:01:04.027 --> 00:01:06.269
Let's do another example.

00:01:06.269 --> 00:01:09.775
Here they say mark all the
relative minimum points

00:01:09.775 --> 00:01:11.502
in the graph.

00:01:11.502 --> 00:01:14.941
Well, a relative minimum
point is a point of the graph

00:01:14.941 --> 00:01:18.140
where if were to look at the
values of the graph around it,

00:01:18.140 --> 00:01:21.159
they're all going to
be the same or higher.

00:01:21.159 --> 00:01:22.059
One way to think about it,

00:01:22.059 --> 00:01:25.047
this would be the bottom
of a dip in the graph.

00:01:25.047 --> 00:01:28.095
And you see one big dip in this graph,

00:01:28.095 --> 00:01:30.130
and the bottom of it is right over there,

00:01:30.130 --> 00:01:32.215
so that would be a relative minimum point.

00:01:32.215 --> 00:01:35.738
And you can see if you have
the X values around it,

00:01:35.738 --> 00:01:38.506
the values of the function at
those X values are all going

00:01:38.506 --> 00:01:40.186
to be the same or higher

00:01:40.186 --> 00:01:42.884
than the value of the
function right at this point.

00:01:42.884 --> 00:01:45.008
That's not true for
any of the other points

00:01:45.008 --> 00:01:47.508
that we can see of this graph.