Interpreting confidence level example

WEBVTT
Kind: captions
Language: en

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- [Instructor] We are
told that a zookeeper

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took a random sample of 30 days

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and observed how much food an elephant ate

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on each of those days.

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The sample mean was 350 kilograms,

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and the sample standard
deviation was 25 kilograms.

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The resulting 90% confidence interval

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for the mean amount of
food was from 341 kilograms

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to 359 kilograms.

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Which of the following statements

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is a correct interpretation
of the 90% confidence level?

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So like always, pause this video

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and see if you can
answer this on your own.

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So before we even look at these choices,

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let's just make sure we're
reading the statement

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or interpreting the statement correctly.

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A zookeeper is trying to figure out

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what the true expected amount

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of food an elephant would eat on a day.

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You could view that as
the mean amount of food

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that an elephant would eat on a day.

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If you view it as the number,

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all the possible days as the population,

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you could view this as the population mean

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for mean amount of food per day.

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Now, the zookeeper doesn't know that,

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and so instead they're
trying to estimate it

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by sampling 30 days.

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So let's think about it this way.

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If I...

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So let's say that this is
the true population mean,

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the true mean amount of food

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that an elephant will eat in a day.

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What the zookeeper can try to do is,

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well, they take a sample.

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In this case, they took
a sample of 30 days.

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And they calculated a sample statistic,

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in this case, the sample
mean of 350 kilograms.

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I don't know if it's actually

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to the right of the true parameter,

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but just for visualization
purposes let's say it is.

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So let's say sample mean, and
this is their first sample,

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it was 350 kilograms.

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And then using the sample,

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they were able to construct
a confidence interval

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from 341 to 359 kilograms.

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And so the confidence interval,
I'll draw it like this.

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We actually aren't sure
if it actually overlaps

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with the true mean like I'm drawing here,

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but just for the sake of
visualization purposes,

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let's say that this one happened to.

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The whole point of a 90% confidence level

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is if I kept doing this,

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so this is our first sample

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and the associated interval
with that first sample.

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And then if I did another sample,

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let's say this is the
mean of that next sample,

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so that's sample mean two,

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and I have an associated
confidence interval.

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And that interval,

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not only the start and
end points will change,

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but the actual width of
the interval might change

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depending on what my sample looks like.

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What a 90% confidence level means,

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that if I keep doing this,

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that 90% of my confidence intervals

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should overlap with the true parameter,

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with the true population mean.

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So, now, with that out of the way,

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let's see which of these
choices are consistent

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with that interpretation.

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Choice A, the elephant
ate between 341 kilograms

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and 359 kilograms on
90% of all of the days.

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No, that is definitely
not what is going on here.

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We're not talking about what's happening

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on 90% of the days, so
let's rule this choice out.

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There is a 0.9 probability
that the true mean amount

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of food is between 341 kilograms

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and 359 kilograms.

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So this one is interesting,
and it is a tempting choice,

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because when we do this one sample,

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you can kind of say, all right,

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if I did a bunch of these samples,

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90% of them, if we have
a 90% confidence interval

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or 90% confidence level, should
overlap with this true mean,

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with the population parameter.

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The reason why this is a
little bit uncomfortable

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is it makes the true mean

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sound almost like a random variable,

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that it could kind of jump around,

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and it's the true mean that kind of

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is either gonna jump into this interval

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or not jump into this interval,

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so it causes a little bit of unease.

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So I'm just gonna put
a question mark here.

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In repeated sampling,

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okay, I like the way
that this is starting.

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In repeated sampling, this
method produces intervals.

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Yep, that's what it does.

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Every time you sample,
you produce an interval.

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That capture the population
mean in about 90% of samples.

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Yeah, that's exactly
what we're talking about.

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If we just kept doing this,

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if we have well-constructed
90% confidence intervals,

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that if we kept doing this,

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90% of these constructed sampled intervals

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should overlap with the true mean.

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So I like this choice.

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But let's just read
choice D to rule it out.

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In repeated sampling, this
method produces a sample mean

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between 341 kilograms and 359 kilograms

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in about 90% of samples.

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No, the confidence interval
does not put a constraint on

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that 90% of the time you
will have a sample mean

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between these values.

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It is not trying to do that.

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It is definitely choice C.


Conditions for valid confidence intervals

WEBVTT
Kind: captions
Language: en

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

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is dig a little bit deeper
into confidence intervals.

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In other videos, we compute
them, we even interpret them,

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but here we're gonna make sure that we are

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making the right assumptions

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so that we can have confidence
in our confidence intervals

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or that we are even calculating
them in the right way

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or in the right context.

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So just as a bit of review,

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a lot of what we do in
confidence intervals is

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we're trying to estimate
some population parameter.

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Let's say it's the proportion,

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maybe it's the proportion that
will vote for a candidate.

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We can't survey everyone
so we take a sample.

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And from that sample,

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maybe we calculate a sample proportion.

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And then using this sample proportion,

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we calculate a confidence interval

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on either side of that sample proportion.

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And what we know is that if we do this

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many, many, many times,

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every time we do it we
are very likely to have a

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different sample proportion.

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So that'd be sample proportion
one, sample proportion two.

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And every time we do it, we might get,

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maybe this is sample proportion two,

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not only will we get a different,

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I guess you can say
center of our interval,

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but the margin of error might change

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because we are using the
sample proportion to calculate.

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But the first assumption,
that has to be true.

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And even (mumbles) any claims
about this confidence interval

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with confidence, is that
your sample is random.

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So that you have a random sample.

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If you're trying to estimate
the proportion of people

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that are gonna vote
for a certain candidate

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but you are only surveying
people at a senior community,

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well, that would not be
a truly random sample,

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if we were only to survey
people on a college campus.

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So like with all things with statistics,

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you really wanna make sure

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that you're dealing with a random sample

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and take great care to do that.

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The second thing that we have to assume,

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and this is sometimes known
as the normal condition,

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normal condition.

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Remember, the whole basis
behind confidence intervals

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is we assume that the distribution

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of the sample proportions,

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the sampling distribution
of the sample proportions,

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has roughly a normal shape like that.

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But in order to make that assumption

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that it's roughly normal,

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we have this normal condition.

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And the rule of thumb here
is that you would expect

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per sample more than 10 successes,

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successes,

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successes, and failures each,

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each.

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So for example, if your
sample size was only 10,

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let's say the true
proportion was 50% or 0.5,

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then you wouldn't meet
that normal condition

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because you would expect five successes

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and five failures for each sample.

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Now, because usually when we're
doing confidence intervals

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we don't even know the
true population parameter,

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what we would actually just do is

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look at our sample and just count

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how many successes and
how many failures we have.

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And if we have less than
10 on either one of those,

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then we are going to have a problem.

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So you wanna have at least
greater than or equal to

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10 successes or failures on each.

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And you actually don't
even have to say expect

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because you're going to get a sample

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and you could just
count how many successes

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and failures you have.

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If you don't see that, then
the normal condition is not met

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and the statements you make
about your confidence interval

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aren't necessarily going to be as valid.

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The last thing we wanna really make sure

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is known as the independence condition.

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Independence condition.

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And this is the 10% rule.

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If we are sampling without replacement,

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and sometimes it's hard to do replacement.

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If you're surveying people who are exiting

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a store, for example,

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you can't ask them to
go back into the store

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or it might be very awkward to
ask to go back in the store.

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And so the independence condition
is that your sample size,

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so sample, let me just say n,

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n is less than 10% of the population size.

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And so let's say your
population were 100,000 people.

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If you surveyed 1,000 people,

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well, that was 1% of the population

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so you'd feel pretty good

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that the independence condition is met.

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And once again, this is
valuable when you are sampling

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without replacement.

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Now, to appreciate how
our confidence intervals

00:04:18.754 --> 00:04:20.688
don't do what we think they're gonna do

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when any of these things are broken,

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and I'll focus on these latter two.

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The random sample condition,

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that's super important
frankly in all of statistics.

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So let's first look at a situation where

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independence condition breaks down.

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So right over here,

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you can see that we are using
our little gumball simulation.

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And in that gumball simulation,

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we have a true population proportion,

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but someone doing these
samples might not know that.

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We're trying to construct
confidence interval

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with 95% confidence level.

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And what we've set up here
is we aren't replacing.

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So every member of our sample,

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we're not looking at it
and putting it back in.

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We're just gonna take a sample of 200.

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And I've set up the
population so that it's a

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far larger than 10% of the population.

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And then when I drew a bunch of samples,

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so this is a situation where I did

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almost 1500 samples here of size 200,

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what you can see here is

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the situations where our
true population parameter

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was contained in the confidence interval

00:05:20.062 --> 00:05:22.540
that we calculated for that sample.

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And then you see in red
the ones where it's not.

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And as you can see, we are
only having a hit so to speak.

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The overlap between
the confidence interval

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that we're calculating in
the true population parameter

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is happening about 93% of the time.

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And this is a pretty
large number of samples.

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If it's truly at a 95% confidence level,

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this should be happening 95% of the time.

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Similarly, we can look at a situation

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where our normal condition breaks down.

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And our normal condition,

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we can see here that our
sample size (mumbles) is 15.

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Actually, if I scroll down a little bit,

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you can see that the
simulation even worries me.

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There are fewer than
10 expected successes.

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And you can see that when I do,

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once again I did a bunch of samples here.

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I did over 2,000 samples.

00:06:05.816 --> 00:06:08.649
Even though I'm trying to set
up these confidence intervals

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that every time I compute
it, that I've overtime,

00:06:12.991 --> 00:06:16.114
that there's kind of a
95% hit rate so to speak,

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here's only a 94% hit rate.

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And I've done a lot of samples here.

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And so the big takeaway,

00:06:21.397 --> 00:06:23.708
not being random will really skew things,

00:06:23.708 --> 00:06:24.990
but if you don't feel good about

00:06:24.990 --> 00:06:27.314
how normal the actual
sampling distribution

00:06:27.314 --> 00:06:28.989
of the sample proportions are

00:06:28.989 --> 00:06:32.239
or if your sample size
is a fairly large chunk

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of your population and
you're not replacing

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and you're violating the
independence condition,

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then your confidence level

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that you think you're computing for

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when you make your confidence
intervals might not be valid.


Confidence intervals and margin of error

WEBVTT
Kind: captions
Language: en

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- [Instructor] It is election season,

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and there is a runoff between candidate A

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versus candidate B.

00:00:06.269 --> 00:00:07.305
And we are pollsters.

00:00:07.305 --> 00:00:08.885
And we're interested
in figuring out, well,

00:00:08.885 --> 00:00:12.150
what's the likelihood that
candidate A wins this election?

00:00:12.150 --> 00:00:15.306
Well, ideally, we would go
to the entire population

00:00:15.306 --> 00:00:17.220
of likely voters right over here,

00:00:17.220 --> 00:00:19.798
let's say there's 100,000 likely voters,

00:00:19.798 --> 00:00:22.910
and we would ask every one of
the them, who do you support?

00:00:22.910 --> 00:00:23.905
And from that,

00:00:23.905 --> 00:00:26.625
we would be able to get
the population proportion,

00:00:26.625 --> 00:00:30.714
which would be, this
is the proportion that

00:00:30.714 --> 00:00:32.358
support,

00:00:32.358 --> 00:00:33.721
support

00:00:33.721 --> 00:00:35.398
candidate A.

00:00:35.398 --> 00:00:36.537
But it might not be realistic.

00:00:36.537 --> 00:00:38.303
In fact, it definitely
will not be realistic

00:00:38.303 --> 00:00:41.164
to ask, well, all 100,000 people.

00:00:41.164 --> 00:00:42.616
So instead, we do the thing

00:00:42.616 --> 00:00:44.341
that we tend to do in statistics is,

00:00:44.341 --> 00:00:46.900
is that we sample this population,

00:00:46.900 --> 00:00:50.158
and we calculate a
statistic from that sample

00:00:50.158 --> 00:00:52.778
in order to estimate this parameter.

00:00:52.778 --> 00:00:55.388
So let's say we take a
sample right over here.

00:00:55.388 --> 00:00:57.237
So this sample size,

00:00:57.237 --> 00:00:59.154
let's say n equals 100.

00:01:00.064 --> 00:01:03.043
And we calculate the sample proportion

00:01:03.043 --> 00:01:04.578
that support candidate A.

00:01:04.578 --> 00:01:07.061
So out of the 100, let's say that 54

00:01:07.061 --> 00:01:09.155
say that they're going
to support candidate A.

00:01:09.155 --> 00:01:12.322
So the sample proportion here is 0.54.

00:01:14.037 --> 00:01:15.819
And just to appreciate

00:01:15.819 --> 00:01:18.300
that we're not always going to get 0.54,

00:01:18.300 --> 00:01:19.360
there could've been a situation

00:01:19.360 --> 00:01:21.216
where we sampled a different 100,

00:01:21.216 --> 00:01:25.059
and we would've maybe gotten
a different sample proportion.

00:01:25.059 --> 00:01:27.642
Maybe in that one, we got 0.58.

00:01:29.430 --> 00:01:32.090
And we already have
the tools in statistics

00:01:32.090 --> 00:01:33.800
to think about this,

00:01:33.800 --> 00:01:36.057
the distribution of the possible

00:01:36.057 --> 00:01:38.153
sample proportions we could get.

00:01:38.153 --> 00:01:39.063
We've talked about it

00:01:39.063 --> 00:01:41.376
when we thought about
sampling distributions.

00:01:41.376 --> 00:01:45.209
So you could have the
sampling distribution of

00:01:47.149 --> 00:01:49.652
the sample proportions,

00:01:49.652 --> 00:01:50.735
of the sample

00:01:52.171 --> 00:01:53.171
proportions,

00:01:54.133 --> 00:01:54.966
proportions.

00:01:54.966 --> 00:01:57.196
And it's going, this
distribution's going to be specific

00:01:57.196 --> 00:01:59.698
to what our sample size is,

00:01:59.698 --> 00:02:01.285
for

00:02:01.285 --> 00:02:02.785
n is equal to 100.

00:02:04.251 --> 00:02:05.809
And so we can describe

00:02:05.809 --> 00:02:07.726
the possible sample
proportions we could get

00:02:07.726 --> 00:02:11.055
and their likelihoods with
this sampling distribution.

00:02:11.055 --> 00:02:12.866
So let me do that.

00:02:12.866 --> 00:02:15.071
So it would look something like this.

00:02:15.071 --> 00:02:16.827
Because our sample size

00:02:16.827 --> 00:02:18.833
is so much smaller than the population,

00:02:18.833 --> 00:02:20.420
it's way less than 10%,

00:02:20.420 --> 00:02:22.834
we can assume that each
person we're asking,

00:02:22.834 --> 00:02:25.543
that it's approximately independent.

00:02:25.543 --> 00:02:28.527
Also, if we make the assumption
that the true proportion

00:02:28.527 --> 00:02:33.122
isn't too close to zero
or not too close to one,

00:02:33.122 --> 00:02:34.216
then we can say that, well, look,

00:02:34.216 --> 00:02:38.383
this sampling distribution is
roughly going to be normal.

00:02:39.464 --> 00:02:42.353
So we'll have a normal, this
kind of bell curve shape.

00:02:42.353 --> 00:02:44.341
And we know a lot about
the sampling distribution

00:02:44.341 --> 00:02:45.872
of the sample proportions.

00:02:45.872 --> 00:02:47.291
We know already, for example,

00:02:47.291 --> 00:02:49.315
and if this is foreign to
you, I encourage you to

00:02:49.315 --> 00:02:51.930
watch the videos on this on Khan Academy,

00:02:51.930 --> 00:02:54.549
that the mean of this
sampling distribution

00:02:54.549 --> 00:02:58.299
is going to be the actual
population proportion.

00:02:58.299 --> 00:03:00.053
And we also know what
the standard deviation

00:03:00.053 --> 00:03:01.417
of this is going to be.

00:03:01.417 --> 00:03:02.428
So,

00:03:02.428 --> 00:03:04.287
let me, maybe that's
one standard deviation.

00:03:04.287 --> 00:03:05.476
This is two standard deviations.

00:03:05.476 --> 00:03:08.930
That's three standard
deviations above the mean.

00:03:08.930 --> 00:03:12.493
That's one standard deviation,
two standard deviations,

00:03:12.493 --> 00:03:14.718
three standard deviations below the mean.

00:03:14.718 --> 00:03:17.729
So this distance, let me do
this in a different color,

00:03:17.729 --> 00:03:20.848
this standard deviation right over here,

00:03:20.848 --> 00:03:24.704
which we denote as the
standard deviation of

00:03:24.704 --> 00:03:29.234
the sample proportions, for
this sampling distribution,

00:03:29.234 --> 00:03:31.022
this is, we've already
seen the formula there.

00:03:31.022 --> 00:03:33.105
It's the square root of p

00:03:34.385 --> 00:03:36.091
times one minus p,

00:03:36.091 --> 00:03:39.291
where p is, once again,
our population proportion

00:03:39.291 --> 00:03:41.236
divided by our sample size.

00:03:41.236 --> 00:03:45.248
That's why it's specific
for n equals 100 here.

00:03:45.248 --> 00:03:47.355
And so in this first scenario,

00:03:47.355 --> 00:03:49.661
let's just focus on this
one right over here,

00:03:49.661 --> 00:03:52.003
when we took a sample size of n equals 100

00:03:52.003 --> 00:03:55.720
and we got the sample proportion of 0.54,

00:03:55.720 --> 00:03:58.116
we could've gotten all
sorts of outcomes here.

00:03:58.116 --> 00:04:00.871
Maybe 0.54 is right over here.

00:04:00.871 --> 00:04:03.390
Maybe 0.54 is right over here.

00:04:03.390 --> 00:04:05.188
And the reason why I
had this uncertainty is

00:04:05.188 --> 00:04:07.260
we actually don't know what the real

00:04:07.260 --> 00:04:09.388
population parameter is,

00:04:09.388 --> 00:04:11.965
what the real population proportion is.

00:04:11.965 --> 00:04:15.814
But let me ask you maybe a
slightly easier question.

00:04:15.814 --> 00:04:16.647
What is,

00:04:17.523 --> 00:04:18.356
what

00:04:19.624 --> 00:04:20.909
is

00:04:20.909 --> 00:04:22.682
the probability,

00:04:22.682 --> 00:04:24.418
probability

00:04:24.418 --> 00:04:25.251
that

00:04:26.568 --> 00:04:28.985
our sample proportion of 0.54

00:04:30.297 --> 00:04:31.130
is within,

00:04:33.080 --> 00:04:36.663
is within two times
two standard deviations

00:04:38.569 --> 00:04:40.178
of p?

00:04:40.178 --> 00:04:43.015
Pause the video, and think about that.

00:04:43.015 --> 00:04:45.531
Well, that's just saying, look,
if I'm gonna take a sample

00:04:45.531 --> 00:04:48.459
and calculate the sample
proportion right over here,

00:04:48.459 --> 00:04:49.905
what's the probability that I'm within

00:04:49.905 --> 00:04:51.838
two standard deviations of the mean?

00:04:51.838 --> 00:04:54.449
Well, that's essentially going to be

00:04:54.449 --> 00:04:56.303
this area right over here.

00:04:56.303 --> 00:04:58.393
And we know, from studying normal curves,

00:04:58.393 --> 00:05:01.572
that approximately 95% of the area

00:05:01.572 --> 00:05:03.784
is within two standard deviations.

00:05:03.784 --> 00:05:07.438
So this is approximately 95%.

00:05:07.438 --> 00:05:11.009
95% of the time that I
take a sample size of 100

00:05:11.009 --> 00:05:14.734
and I calculate this sample proportion,

00:05:14.734 --> 00:05:15.797
95% of the time,

00:05:15.797 --> 00:05:19.379
I'm going to be within
two standard deviations.

00:05:19.379 --> 00:05:20.970
But if you take this statement,

00:05:20.970 --> 00:05:22.720
you can actually construct
another statement

00:05:22.720 --> 00:05:25.369
that starts to feel a little bit more,

00:05:25.369 --> 00:05:27.849
I guess we could say inferential.

00:05:27.849 --> 00:05:29.432
We could say there,

00:05:30.916 --> 00:05:31.749
there is

00:05:32.647 --> 00:05:33.480
a 95%

00:05:35.538 --> 00:05:36.455
probability

00:05:37.464 --> 00:05:38.688
that

00:05:38.688 --> 00:05:41.188
the population proportion p is

00:05:42.248 --> 00:05:43.875
within,

00:05:43.875 --> 00:05:46.458
within two standard deviations,

00:05:47.365 --> 00:05:50.825
two standard deviations of p-hat,

00:05:50.825 --> 00:05:53.334
which is equal to 0.54.

00:05:53.334 --> 00:05:54.167
Pause this video.

00:05:54.167 --> 00:05:57.043
Appreciate that these two
are equivalent statements.

00:05:57.043 --> 00:06:00.768
If there's a 95% chance
that our sample proportion

00:06:00.768 --> 00:06:04.418
is within two standard deviations
of the true proportion,

00:06:04.418 --> 00:06:07.428
well, that's equivalent to
saying that there's a 95% chance

00:06:07.428 --> 00:06:10.988
that our true proportion is
within two standard deviations

00:06:10.988 --> 00:06:13.519
of our sample proportion.

00:06:13.519 --> 00:06:15.625
And this is really, really interesting

00:06:15.625 --> 00:06:19.452
because if we were able to
figure out what this value is,

00:06:19.452 --> 00:06:21.346
well, then we would be able to create

00:06:21.346 --> 00:06:23.972
what you could call a confidence interval.

00:06:23.972 --> 00:06:26.732
Now, you immediately might
be seeing a problem here.

00:06:26.732 --> 00:06:28.565
In order to calculate this,

00:06:28.565 --> 00:06:31.291
our standard deviation
of this distribution,

00:06:31.291 --> 00:06:34.476
we have to know our population parameter.

00:06:34.476 --> 00:06:35.767
So pause this video,

00:06:35.767 --> 00:06:37.790
and think about what we would do instead.

00:06:37.790 --> 00:06:39.695
If we don't know what p is here,

00:06:39.695 --> 00:06:41.672
if we don't know our
population proportion,

00:06:41.672 --> 00:06:45.069
do we have something that
we could use as an estimate

00:06:45.069 --> 00:06:47.691
for our population proportion?

00:06:47.691 --> 00:06:50.193
Well, yes, we calculated p-hat already.

00:06:50.193 --> 00:06:52.697
We calculated our sample proportion.

00:06:52.697 --> 00:06:54.876
And so a new statistic
that we could define

00:06:54.876 --> 00:06:56.881
is the standard error,

00:06:56.881 --> 00:07:01.178
the standard error of
our sample proportions.

00:07:01.178 --> 00:07:05.369
And we can define that as being equal to,

00:07:05.369 --> 00:07:08.011
since we don't know the
population proportion,

00:07:08.011 --> 00:07:09.564
we're going to use the sample proportion,

00:07:09.564 --> 00:07:12.636
p-hat times one minus p-hat,

00:07:12.636 --> 00:07:14.145
all of that over n.

00:07:14.145 --> 00:07:16.057
In this case, of course, n is 100.

00:07:16.057 --> 00:07:17.472
We do know that.

00:07:17.472 --> 00:07:18.482
And it actually turns out,

00:07:18.482 --> 00:07:20.142
I'm not going to prove it in this video,

00:07:20.142 --> 00:07:22.561
that this actually is
an unbiased estimator

00:07:22.561 --> 00:07:24.293
for this right over here.

00:07:24.293 --> 00:07:27.293
So this is going to be equal to 0.54

00:07:28.691 --> 00:07:30.774
times one minus 0.54,

00:07:30.774 --> 00:07:31.857
so it's 0.46,

00:07:33.557 --> 00:07:35.307
all of that over 100.

00:07:36.887 --> 00:07:39.637
So we have the square root of .54

00:07:41.752 --> 00:07:42.585
times .46

00:07:44.132 --> 00:07:45.382
divided by 100,

00:07:46.791 --> 00:07:49.284
close my parentheses, Enter.

00:07:49.284 --> 00:07:52.144
So if I round to the nearest
hundredth, it's going to be,

00:07:52.144 --> 00:07:53.635
actually, even if I round
to the nearest thousandth,

00:07:53.635 --> 00:07:56.192
it's going to be approximately 5/100.

00:07:56.192 --> 00:07:58.109
So this is going to be,

00:07:58.953 --> 00:08:01.203
this is approximately 0.05.

00:08:03.786 --> 00:08:07.765
So another way to say all
of these things is, instead,

00:08:07.765 --> 00:08:09.636
we don't know exactly this,

00:08:09.636 --> 00:08:11.795
but now we have an estimate for it.

00:08:11.795 --> 00:08:13.795
So we could now say with

00:08:15.011 --> 00:08:15.844
95%

00:08:16.912 --> 00:08:19.617
confidence, and that will often be known

00:08:19.617 --> 00:08:21.997
as our confidence level right over here,

00:08:21.997 --> 00:08:24.747
with 95% confidence between,

00:08:26.657 --> 00:08:27.490
between,

00:08:28.550 --> 00:08:31.480
and so we'd want to go two standard errors

00:08:31.480 --> 00:08:33.379
below our sample proportion

00:08:33.379 --> 00:08:35.193
that we just happened to calculate.

00:08:35.193 --> 00:08:39.564
So that would be 0.54
minus two times 5/100.

00:08:39.564 --> 00:08:43.140
So that would be 0.54 minus 10/100,

00:08:43.140 --> 00:08:44.807
which would be 0.44.

00:08:46.157 --> 00:08:48.738
And we'd also want to
go two standard errors

00:08:48.738 --> 00:08:50.700
above the sample proportion.

00:08:50.700 --> 00:08:53.338
So that would be that plus 10/100.

00:08:53.338 --> 00:08:54.171
And 0.64

00:08:56.621 --> 00:08:58.081
of voters,

00:08:58.081 --> 00:08:59.183
of

00:08:59.183 --> 00:09:00.016
voters

00:09:00.871 --> 00:09:01.704
support,

00:09:02.636 --> 00:09:04.182
support

00:09:04.182 --> 00:09:05.278
A.

00:09:05.278 --> 00:09:07.725
And so this interval that
we have right over here,

00:09:07.725 --> 00:09:08.558
from 0.44

00:09:09.486 --> 00:09:11.095
to 0.64,

00:09:11.095 --> 00:09:13.593
this will be known as
our confidence interval,

00:09:13.593 --> 00:09:14.426
confidence

00:09:15.792 --> 00:09:17.112
interval.

00:09:17.112 --> 00:09:18.263
And this will change,

00:09:18.263 --> 00:09:20.788
not just in the starting
point and the end point,

00:09:20.788 --> 00:09:22.677
but it will change the actual length

00:09:22.677 --> 00:09:23.867
of our confidence interval,

00:09:23.867 --> 00:09:25.525
will change depending on

00:09:25.525 --> 00:09:28.365
what sample proportion we happened to pick

00:09:28.365 --> 00:09:30.762
for that sample of 100.

00:09:30.762 --> 00:09:33.142
A related idea to the confidence interval

00:09:33.142 --> 00:09:35.746
is this notion of margin of error,

00:09:35.746 --> 00:09:36.579
margin

00:09:37.800 --> 00:09:39.337
of error.

00:09:39.337 --> 00:09:41.543
And for this particular case,

00:09:41.543 --> 00:09:43.192
for this particular sample,

00:09:43.192 --> 00:09:44.421
our margin of error,

00:09:44.421 --> 00:09:47.488
because we care about 95% confidence,

00:09:47.488 --> 00:09:49.577
so that would be two standard errors.

00:09:49.577 --> 00:09:52.853
So our margin of error here is
two times our standard error,

00:09:52.853 --> 00:09:55.020
would just be 0.1 or 0.10.

00:09:56.842 --> 00:09:59.535
And so we're going one margin of error

00:09:59.535 --> 00:10:02.273
above our sample
proportion right over here

00:10:02.273 --> 00:10:03.387
and one margin of error

00:10:03.387 --> 00:10:05.853
below our sample
proportion right over here

00:10:05.853 --> 00:10:07.518
to define our confidence interval.

00:10:07.518 --> 00:10:09.780
And as I mentioned, this
margin of error is not going

00:10:09.780 --> 00:10:12.373
to be fixed every time we take a sample.

00:10:12.373 --> 00:10:14.826
Depending on what our
sample proportion is,

00:10:14.826 --> 00:10:16.954
it's going to affect our margin of error

00:10:16.954 --> 00:10:19.117
because that is calculated, essentially,

00:10:19.117 --> 00:10:20.960
with the standard error.

00:10:20.960 --> 00:10:23.937
Another interpretation of this is

00:10:23.937 --> 00:10:25.558
that the method that we used

00:10:25.558 --> 00:10:27.363
to get this interval right over here,

00:10:27.363 --> 00:10:30.399
the method that we used
to get this confidence,

00:10:30.399 --> 00:10:32.428
to get this confidence interval,

00:10:32.428 --> 00:10:35.216
when we use it over and over,

00:10:35.216 --> 00:10:37.417
it will produce intervals,

00:10:37.417 --> 00:10:38.886
and the intervals won't
always be the same.

00:10:38.886 --> 00:10:41.044
It's gonna be dependent
on our sample proportion,

00:10:41.044 --> 00:10:42.731
but it will produce intervals

00:10:42.731 --> 00:10:44.932
which include the true proportion,

00:10:44.932 --> 00:10:47.006
which we might not know
and often don't know.

00:10:47.006 --> 00:10:51.173
It'll include the true
proportion 95% of the time.

00:10:52.056 --> 00:10:55.245
I'll cover that intuition
more in future videos.

00:10:55.245 --> 00:10:56.843
We'll see how the interval changes,

00:10:56.843 --> 00:10:58.558
how the margin of error changes.

00:10:58.558 --> 00:11:00.381
But when you do this calculation

00:11:00.381 --> 00:11:02.951
over and over and over again,

00:11:02.951 --> 00:11:05.263
95% of the time,

00:11:05.263 --> 00:11:08.476
your true proportion is
going to be contained

00:11:08.476 --> 00:11:12.930
in whatever interval you
happen to calculate that time.

00:11:12.930 --> 00:11:14.641
Now, another interesting question is,

00:11:14.641 --> 00:11:16.384
is, well, what if you wanted to

00:11:16.384 --> 00:11:18.490
tighten up the intervals on average?

00:11:18.490 --> 00:11:20.069
How would you do that?

00:11:20.069 --> 00:11:22.848
Well, if you wanted to
lower your margin of error,

00:11:22.848 --> 00:11:24.971
the best way to lower the margin of error

00:11:24.971 --> 00:11:28.054
is if you increase this
denominator right over here.

00:11:28.054 --> 00:11:29.736
And increasing that denominator means

00:11:29.736 --> 00:11:31.457
increasing the sample size.

00:11:31.457 --> 00:11:33.133
And so one thing that you will often see

00:11:33.133 --> 00:11:36.122
when people are talking
about election coverage is,

00:11:36.122 --> 00:11:37.982
well, we need to sample more people

00:11:37.982 --> 00:11:41.066
in order to get a lower margin of error.

00:11:41.066 --> 00:11:41.899
But I'll leave you there,

00:11:41.899 --> 00:11:44.095
and I'll see you in future videos.


Confidence interval simulation

WEBVTT
Kind: captions
Language: en

00:00:00.290 --> 00:00:01.313
- [Instructor] The goal of this video

00:00:01.313 --> 00:00:03.401
is to use this scratch pad on Khan Academy

00:00:03.401 --> 00:00:05.802
that was written by Khan
Academy user Charlotte Allen,

00:00:05.802 --> 00:00:07.109
in order to get a better

00:00:07.109 --> 00:00:09.903
intuitive sense of confidence intervals.

00:00:09.903 --> 00:00:13.624
So here we're dealing
with a gumball machine

00:00:13.624 --> 00:00:16.042
where a certain proportion of the gumballs

00:00:16.042 --> 00:00:17.482
are going to be green.

00:00:17.482 --> 00:00:19.202
And so let's say we can set that on it.

00:00:19.202 --> 00:00:21.834
Let's make that 60% of
the gumballs are green.

00:00:21.834 --> 00:00:23.165
But let's say someone else comes along

00:00:23.165 --> 00:00:24.095
and they don't actually know

00:00:24.095 --> 00:00:26.420
the proportion of gumballs that are green,

00:00:26.420 --> 00:00:28.333
but they can take samples.

00:00:28.333 --> 00:00:31.355
And so let's say they take
samples of 50 at a time,

00:00:31.355 --> 00:00:33.602
and so they draw a sample.

00:00:33.602 --> 00:00:35.444
The sample proportion right over here,

00:00:35.444 --> 00:00:38.366
actually just happened to be 0.6,

00:00:38.366 --> 00:00:39.878
but then they could draw another sample.

00:00:39.878 --> 00:00:41.669
This time the sample proportion

00:00:41.669 --> 00:00:45.801
is 0.52 or 52% of those 50 gumballs

00:00:45.801 --> 00:00:47.620
happened to be green.

00:00:47.620 --> 00:00:48.612
Now you could say, all right,

00:00:48.612 --> 00:00:50.453
well, these are all different estimates.

00:00:50.453 --> 00:00:52.656
But for any given estimate,

00:00:52.656 --> 00:00:56.117
what, how confident are we that the,

00:00:56.117 --> 00:00:58.140
a certain range around that estimate

00:00:58.140 --> 00:01:01.755
actually contains the true
population proportion?

00:01:01.755 --> 00:01:03.624
And so if we look at
this tab right over here,

00:01:03.624 --> 00:01:05.906
that's what confidence
intervals are good for.

00:01:05.906 --> 00:01:06.970
And in a previous video,

00:01:06.970 --> 00:01:09.649
we talked about how you calculate
the confidence interval.

00:01:09.649 --> 00:01:11.901
What we wanna do is say, well,

00:01:11.901 --> 00:01:14.124
there's a 95% chance,

00:01:14.124 --> 00:01:15.814
and we get that from
this confidence level,

00:01:15.814 --> 00:01:18.904
and 95% is the confidence
level people typically use.

00:01:18.904 --> 00:01:21.957
And so there's a 95% chance that

00:01:21.957 --> 00:01:23.924
whatever our sample proportion is

00:01:23.924 --> 00:01:25.535
that it's within two standard deviations

00:01:25.535 --> 00:01:27.508
of the true proportion.

00:01:27.508 --> 00:01:30.573
Or that the true proportion
is going to be contained

00:01:30.573 --> 00:01:33.196
in an interval that are
two standard deviations

00:01:33.196 --> 00:01:36.466
on either side of our sample proportion.

00:01:36.466 --> 00:01:38.473
Well if you don't know
the true proportion,

00:01:38.473 --> 00:01:41.206
the way that you estimate
the standard deviation

00:01:41.206 --> 00:01:42.632
is with a standard error,

00:01:42.632 --> 00:01:44.069
which we've done in previous videos.

00:01:44.069 --> 00:01:46.354
And so this is two standard
errors to the right

00:01:46.354 --> 00:01:47.774
and two standard errors to the left

00:01:47.774 --> 00:01:49.773
of our sample proportion.

00:01:49.773 --> 00:01:51.916
And our confidence interval
is this entire interval,

00:01:51.916 --> 00:01:54.095
going from this left
point to this right point.

00:01:54.095 --> 00:01:55.725
And as we draw more samples,

00:01:55.725 --> 00:01:58.193
you can see it's not obvious,

00:01:58.193 --> 00:02:01.134
but our intervals change depending on

00:02:01.134 --> 00:02:03.314
what our actual sample proportion is.

00:02:03.314 --> 00:02:05.132
Because we use our sample proportion

00:02:05.132 --> 00:02:07.480
to calculate our confidence interval

00:02:07.480 --> 00:02:09.437
because we're assuming
whoever's doing the sampling

00:02:09.437 --> 00:02:13.984
does not actually know the
true population proportion.

00:02:13.984 --> 00:02:15.503
Now what's interesting here,

00:02:15.503 --> 00:02:17.285
about this simulation,

00:02:17.285 --> 00:02:20.541
is that we can see what
percentage of the time

00:02:20.541 --> 00:02:22.842
does our confidence interval,

00:02:22.842 --> 00:02:25.768
does it actually contain
the true parameter?

00:02:25.768 --> 00:02:28.616
So let me just draw out
25 samples at a time.

00:02:28.616 --> 00:02:30.911
And so you can see here that right now,

00:02:30.911 --> 00:02:34.022
93% of our,

00:02:34.022 --> 00:02:36.363
for 93% of our samples,

00:02:36.363 --> 00:02:40.110
did our confidence
interval actually contain

00:02:40.110 --> 00:02:41.997
our population parameter.

00:02:41.997 --> 00:02:45.150
And we can keep sampling over here

00:02:45.150 --> 00:02:48.148
and we can see the more
samples that we take,

00:02:48.148 --> 00:02:50.016
it really is approaching

00:02:50.016 --> 00:02:53.581
that close to 95% of the time,

00:02:53.581 --> 00:02:56.104
our confidence interval does indeed

00:02:56.104 --> 00:02:58.494
contain the true parameter.

00:02:58.494 --> 00:03:00.528
And so once again, we did all that math

00:03:00.528 --> 00:03:01.879
in the previous video,

00:03:01.879 --> 00:03:04.995
but here you can see
that confidence intervals

00:03:04.995 --> 00:03:07.300
calculated the way that
we calculated them,

00:03:07.300 --> 00:03:09.355
actually do a pretty good job

00:03:09.355 --> 00:03:10.942
of what they claim to do.

00:03:10.942 --> 00:03:13.013
That if we calculate a confidence interval

00:03:13.013 --> 00:03:15.768
based on a confidence level of 95%,

00:03:15.768 --> 00:03:17.530
that it is indeed the case that

00:03:17.530 --> 00:03:20.143
roughly 95% of the time,

00:03:20.143 --> 00:03:23.368
the true parameter, the
population proportion

00:03:23.368 --> 00:03:25.867
will be contained in that interval.

00:03:25.867 --> 00:03:28.368
And I could just draw more
and more and more samples

00:03:28.368 --> 00:03:30.891
and we can actually see that happening.

00:03:30.891 --> 00:03:32.186
Every now and then, for sure,

00:03:32.186 --> 00:03:34.839
you get a sample where

00:03:34.839 --> 00:03:37.041
even when you calculate
your confidence interval,

00:03:37.041 --> 00:03:39.407
the true parameter, the
true population proportion

00:03:39.407 --> 00:03:40.823
is not contained.

00:03:40.823 --> 00:03:43.891
But that is the exception,
that happens very infrequently.

00:03:43.891 --> 00:03:47.019
95% of the time, your
true population parameter

00:03:47.019 --> 00:03:49.107
is contained in that interval.

00:03:49.107 --> 00:03:51.411
Now another interesting thing to see is,

00:03:51.411 --> 00:03:53.257
if we increase our sample size,

00:03:53.257 --> 00:03:55.894
our confidence interval
is going to get narrower.

00:03:55.894 --> 00:03:57.340
So if we increase our sample size,

00:03:57.340 --> 00:03:58.936
we'll just make it 200.

00:03:58.936 --> 00:04:00.503
Now let's draw some samples.

00:04:00.503 --> 00:04:04.569
Notice, now our confidence
intervals are narrower,

00:04:04.569 --> 00:04:06.709
but still because our confidence level,

00:04:06.709 --> 00:04:08.406
which was used to
calculate these intervals,

00:04:08.406 --> 00:04:09.859
is still 95%,

00:04:09.859 --> 00:04:11.727
when we draw a bunch of samples,

00:04:11.727 --> 00:04:13.398
we are still going to get

00:04:13.398 --> 00:04:16.034
roughly 95% of the time

00:04:16.034 --> 00:04:18.781
our confidence intervals contain

00:04:18.781 --> 00:04:20.854
our true population proportion.

00:04:20.854 --> 00:04:24.077
But roughly 5% of the time, they don't.


Scarcity of resources

WEBVTT
Kind: captions
Language: en

00:00:00.276 --> 00:00:01.637
- [Instructor] All of economics is based

00:00:01.637 --> 00:00:05.172
on this notion of scarcity of resources.

00:00:05.172 --> 00:00:06.270
What does scarcity mean?

00:00:06.270 --> 00:00:08.211
Well, in an everyday context, it means

00:00:08.211 --> 00:00:10.263
that there's not as much of something,

00:00:10.263 --> 00:00:13.178
say, a resource, as people may need

00:00:13.178 --> 00:00:15.993
or there's not an unlimited
amount of something.

00:00:15.993 --> 00:00:17.326
So not unlimited

00:00:19.070 --> 00:00:20.403
unlimited amount

00:00:22.291 --> 00:00:24.541
of a resource or resources.

00:00:25.806 --> 00:00:28.019
Resource, and I'll put a little,

00:00:28.019 --> 00:00:29.980
resource or resources.

00:00:29.980 --> 00:00:32.491
And the common examples, especially

00:00:32.491 --> 00:00:34.339
in an academic economics class,

00:00:34.339 --> 00:00:36.360
when people are talking about scarcity,

00:00:36.360 --> 00:00:38.391
the resource they're talking about,

00:00:38.391 --> 00:00:40.809
they'll often say land.

00:00:40.809 --> 00:00:42.892
And by saying land,
they're speaking generally

00:00:42.892 --> 00:00:45.452
of natural resources.

00:00:45.452 --> 00:00:49.619
And so, examples of this
would be things like energy.

00:00:51.130 --> 00:00:54.097
It could even be things like water.

00:00:54.097 --> 00:00:56.404
It could be lumber.

00:00:56.404 --> 00:01:00.984
It could be minerals,
maybe some type of metal.

00:01:00.984 --> 00:01:02.914
Obviously, it could be land itself.

00:01:02.914 --> 00:01:04.824
And you could see some of that depicted

00:01:04.824 --> 00:01:06.482
in a picture like this.

00:01:06.482 --> 00:01:09.740
Clearly, there's land here
and you can even argue

00:01:09.740 --> 00:01:12.525
maybe, even the solar energy
that it has access to,

00:01:12.525 --> 00:01:16.304
that these would all be
broadly put into this category.

00:01:16.304 --> 00:01:18.550
Now another type of natural resource

00:01:18.550 --> 00:01:21.017
that is often talked about
in an economics class

00:01:21.017 --> 00:01:22.184
will be labor.

00:01:23.667 --> 00:01:26.494
And labor we associate with people working

00:01:26.494 --> 00:01:28.921
and that is what labor
is making reference to.

00:01:28.921 --> 00:01:31.171
It's all about work effort.

00:01:32.833 --> 00:01:34.256
And we talk about work effort,

00:01:34.256 --> 00:01:35.830
we're talking about the workers

00:01:35.830 --> 00:01:40.646
and how much they're
working, so hours of labor.

00:01:40.646 --> 00:01:41.896
Hours of labor.

00:01:43.429 --> 00:01:44.953
And this picture right over here

00:01:44.953 --> 00:01:47.592
is a clear picture of some workers.

00:01:47.592 --> 00:01:51.324
Now, another resource that
you'll often talk about

00:01:51.324 --> 00:01:55.195
in the context of scarcity is capital.

00:01:55.195 --> 00:01:57.560
And capital can be a little
bit confusing at first.

00:01:57.560 --> 00:01:59.552
Well, it's things that people make

00:01:59.552 --> 00:02:02.092
in order to make other things.

00:02:02.092 --> 00:02:02.925
So things

00:02:04.907 --> 00:02:05.907
made to make

00:02:09.385 --> 00:02:10.468
other things.

00:02:12.271 --> 00:02:15.615
And so just to hit the point
home here, pause this video.

00:02:15.615 --> 00:02:19.282
In these pictures, what
capital do you actually see?

00:02:19.282 --> 00:02:20.867
Well, there's actually a bunch of capital

00:02:20.867 --> 00:02:22.240
in these pictures.

00:02:22.240 --> 00:02:25.640
There's some of the obvious
things like these tools,

00:02:25.640 --> 00:02:28.518
this would be a clear example of capital.

00:02:28.518 --> 00:02:31.139
Even these buildings,
these buildings are used

00:02:31.139 --> 00:02:33.280
to maybe store animals or crops.

00:02:33.280 --> 00:02:34.999
So these are things that someone made

00:02:34.999 --> 00:02:37.112
in order to help make other things.

00:02:37.112 --> 00:02:38.848
And some of maybe, the less obvious things

00:02:38.848 --> 00:02:40.514
you might not even notice it at first

00:02:40.514 --> 00:02:41.906
but there's these power lines here.

00:02:41.906 --> 00:02:44.913
Someone made this in order
to help us distribute energy

00:02:44.913 --> 00:02:47.329
which could be used to make other things.

00:02:47.329 --> 00:02:49.309
So that too could be used,

00:02:49.309 --> 00:02:51.797
that could be an example of capital here.

00:02:51.797 --> 00:02:55.105
Now the fourth resource that
you'll hear folks talk about

00:02:55.105 --> 00:02:57.285
is really thinking about
well how do we know

00:02:57.285 --> 00:03:00.588
how to combine these first
three types of resources

00:03:00.588 --> 00:03:04.651
and we could call that entrepreneurship.

00:03:04.651 --> 00:03:06.068
Entrepreneurship.

00:03:07.494 --> 00:03:10.970
Sometimes people will refer to technology

00:03:10.970 --> 00:03:13.600
but this is all how to combine,

00:03:13.600 --> 00:03:14.767
how to combine

00:03:17.085 --> 00:03:18.519
all of the above right over here,

00:03:18.519 --> 00:03:20.551
one through three, these types

00:03:20.551 --> 00:03:22.806
of resources right over here.

00:03:22.806 --> 00:03:25.772
Someone had to decide that
hey these were good places

00:03:25.772 --> 00:03:27.743
to put these storage houses.

00:03:27.743 --> 00:03:30.890
Someone had to decide where
to put the power lines.

00:03:30.890 --> 00:03:34.353
Someone had to decide
what crops to plant here

00:03:34.353 --> 00:03:35.452
and how to plant them.

00:03:35.452 --> 00:03:37.841
Someone had to decide,
well, what type of labor

00:03:37.841 --> 00:03:39.736
do we need, what type of land,

00:03:39.736 --> 00:03:41.620
what type of capital, the
actual factory building,

00:03:41.620 --> 00:03:43.600
the factory equipment do we need

00:03:43.600 --> 00:03:46.210
in order to produce whatever these folks

00:03:46.210 --> 00:03:47.753
are producing right over here.

00:03:47.753 --> 00:03:49.471
And that general notion,

00:03:49.471 --> 00:03:51.594
you could talk about as entrepreneurship.

00:03:51.594 --> 00:03:52.815
And so the big picture here

00:03:52.815 --> 00:03:54.327
is think about the world around you.

00:03:54.327 --> 00:03:56.754
There's not an unlimited amount of land,

00:03:56.754 --> 00:03:58.045
especially if you're thinking about land

00:03:58.045 --> 00:03:59.244
for a specific purpose.

00:03:59.244 --> 00:04:01.753
There's not an unlimited
amount of natural resources,

00:04:01.753 --> 00:04:04.506
energy, lumber, some type of metal,

00:04:04.506 --> 00:04:06.346
there's not an unlimited amount of labor,

00:04:06.346 --> 00:04:09.069
there's only so many people who exist,

00:04:09.069 --> 00:04:11.434
and there's not an
unlimited amount of capital,

00:04:11.434 --> 00:04:12.979
we don't have an infinite
number of buildings

00:04:12.979 --> 00:04:15.510
or equipment, and we don't have

00:04:15.510 --> 00:04:17.216
an infinite amount of entrepreneurship,

00:04:17.216 --> 00:04:18.537
we can only have so much energy

00:04:18.537 --> 00:04:21.796
to think about how do we put
these other things together.

00:04:21.796 --> 00:04:23.300
So I will leave you there

00:04:23.300 --> 00:04:26.226
and as we go further in
our quest in economics,

00:04:26.226 --> 00:04:29.526
we're gonna see the scarcity
of these four resources

00:04:29.526 --> 00:04:31.859
show up over and over again.


Production Possibilities Curve as a model of a country's economy

WEBVTT
Kind: captions
Language: en

00:00:00.306 --> 00:00:02.073
- [Instructor] Let's say
that we have some country,

00:00:02.073 --> 00:00:04.929
let's call it Utenslandia,
that can only produce

00:00:04.929 --> 00:00:08.464
one of two goods or some
combination of them.

00:00:08.464 --> 00:00:10.547
So it can produces forks,

00:00:12.428 --> 00:00:15.508
or it could produce spoons.

00:00:15.508 --> 00:00:17.882
And so this axis is the quantity forks,

00:00:17.882 --> 00:00:19.668
this axis is the quantity of spoons

00:00:19.668 --> 00:00:21.944
and let's say that if it
puts all of its energy

00:00:21.944 --> 00:00:24.788
into forks, well it would
produce that many forks

00:00:24.788 --> 00:00:27.836
and no spoons, and but
then if tried to focus

00:00:27.836 --> 00:00:31.493
some of its energy, some
of its resources on spoons,

00:00:31.493 --> 00:00:33.850
well then it would produce fewer forks

00:00:33.850 --> 00:00:35.882
and then the more spoons it produces,

00:00:35.882 --> 00:00:38.076
it will produce fewer and fewer forks

00:00:38.076 --> 00:00:41.706
all the way to the point that
if it only focused on spoons,

00:00:41.706 --> 00:00:42.997
well it could produce that many

00:00:42.997 --> 00:00:45.099
but then it would produce no forks.

00:00:45.099 --> 00:00:46.878
What this curve is, and we touched on it

00:00:46.878 --> 00:00:51.295
on other videos, this is the
production possibilities curve

00:00:51.295 --> 00:00:55.989
for our country of Utenslandia
that makes utensils

00:00:55.989 --> 00:00:58.508
and obviously, most countries
are much more complex,

00:00:58.508 --> 00:01:01.100
they don't only produce some
combination of two things

00:01:01.100 --> 00:01:03.761
but this helps us, this is a nice model

00:01:03.761 --> 00:01:06.951
for understanding what
countries might be capable of.

00:01:06.951 --> 00:01:09.754
Now one way to understand this production

00:01:09.754 --> 00:01:12.337
possibilities curve is it shows

00:01:13.256 --> 00:01:15.819
what can be efficiently
produced by this country.

00:01:15.819 --> 00:01:19.711
If it efficiently utilized
all of its resources,

00:01:19.711 --> 00:01:23.488
then it will produce some
combination of forks and spoons

00:01:23.488 --> 00:01:27.217
that sit on the production
possibilities curve.

00:01:27.217 --> 00:01:28.996
So this point right over here,

00:01:28.996 --> 00:01:31.292
this combination of spoons which would be

00:01:31.292 --> 00:01:35.019
that many spoons and that many forks,

00:01:35.019 --> 00:01:38.565
this combination over here,
this would be efficient.

00:01:38.565 --> 00:01:40.678
That point x would be

00:01:40.678 --> 00:01:44.537
an efficient production for Utenslandia.

00:01:44.537 --> 00:01:48.040
So at this point right over
here, let's call that point y.

00:01:48.040 --> 00:01:50.826
Now what happens if Utenslandia goes

00:01:50.826 --> 00:01:52.817
into some type of recession.

00:01:52.817 --> 00:01:56.262
For whatever reason, it's
not able to use its resources

00:01:56.262 --> 00:01:58.323
as efficiently, and we're
talking about resources,

00:01:58.323 --> 00:02:00.204
we're talking about
land, we're talking about

00:02:00.204 --> 00:02:01.849
maybe its factories, we're talking about

00:02:01.849 --> 00:02:04.084
the materials it has, maybe its labor,

00:02:04.084 --> 00:02:05.445
well on that situation, let's say

00:02:05.445 --> 00:02:07.233
it was operating efficiently here

00:02:07.233 --> 00:02:09.550
but then the recession happens

00:02:09.550 --> 00:02:11.913
and so it then it
operates right over here,

00:02:11.913 --> 00:02:14.069
let's call this point right over here z,

00:02:14.069 --> 00:02:17.270
this would be an inefficient
use of its resources,

00:02:17.270 --> 00:02:19.758
sitting behind the production
possibilities curve.

00:02:19.758 --> 00:02:23.739
So this is inefficient, just like that.

00:02:23.739 --> 00:02:25.232
And so one question you might have

00:02:25.232 --> 00:02:28.199
is well what about points that are beyond

00:02:28.199 --> 00:02:29.754
the production possibilities curve

00:02:29.754 --> 00:02:33.391
like point, let's just call
that point a right over there.

00:02:33.391 --> 00:02:34.946
What about that point?

00:02:34.946 --> 00:02:37.688
Well, unless you have more inputs,

00:02:37.688 --> 00:02:39.852
unless you have more land, more capital,

00:02:39.852 --> 00:02:43.111
more labor, if you don't
change the resources here,

00:02:43.111 --> 00:02:43.944
this is actually going to be

00:02:43.944 --> 00:02:47.564
an unattainable point for Utenslandia.

00:02:47.564 --> 00:02:49.372
But let's say you really wanna reach it,

00:02:49.372 --> 00:02:50.803
how can that happen?

00:02:50.803 --> 00:02:53.363
Well, you can actually have investment

00:02:53.363 --> 00:02:56.431
or you could have more land or more labor.

00:02:56.431 --> 00:02:59.560
So let's think about that scenario.

00:02:59.560 --> 00:03:01.530
So let me draw the two axes.

00:03:01.530 --> 00:03:04.395
So that's my fork axis,
that's the quantity of forks

00:03:04.395 --> 00:03:06.569
that Utenslandia will produce in the year.

00:03:06.569 --> 00:03:10.402
This will be the spoon
axis, right over there.

00:03:12.168 --> 00:03:16.557
And let's draw our original
production possibilities curve.

00:03:16.557 --> 00:03:18.304
So I'll try to make it look pretty similar

00:03:18.304 --> 00:03:20.547
to what we had before.

00:03:20.547 --> 00:03:23.078
So that's our original
production possibilities curve.

00:03:23.078 --> 00:03:24.135
Another way of thinking about it

00:03:24.135 --> 00:03:25.444
is it's showing the trade off

00:03:25.444 --> 00:03:28.097
between producing forks and spoons.

00:03:28.097 --> 00:03:29.608
You can actually think about

00:03:29.608 --> 00:03:31.693
what is the opportunity cost of producing

00:03:31.693 --> 00:03:33.989
an incremental spoon in terms of forks.

00:03:33.989 --> 00:03:35.817
How many forks do you have to trade off

00:03:35.817 --> 00:03:37.382
because remember,
there's scarcity at play.

00:03:37.382 --> 00:03:39.708
You don't have an infinite amount of metal

00:03:39.708 --> 00:03:42.464
to produce things with, an
infinite amount of labor,

00:03:42.464 --> 00:03:44.130
an infinite amount of factories.

00:03:44.130 --> 00:03:46.871
But let's say Utenslandia,
they are able to get

00:03:46.871 --> 00:03:49.392
some more land on which
to build factories,

00:03:49.392 --> 00:03:51.342
maybe they build some more factories

00:03:51.342 --> 00:03:53.057
so capital goes up, maybe some people

00:03:53.057 --> 00:03:55.059
migrate to Utenslandia.

00:03:55.059 --> 00:03:58.712
So in that situation,
you would have growth

00:03:58.712 --> 00:04:01.562
and your production possibilities curve

00:04:01.562 --> 00:04:04.560
would actually shift outward.

00:04:04.560 --> 00:04:06.601
So here, we are showing,

00:04:06.601 --> 00:04:08.339
let me make it a little bit,

00:04:08.339 --> 00:04:11.042
we are showing a
situation right over here,

00:04:11.042 --> 00:04:13.732
this is still a production
possibilities curve

00:04:13.732 --> 00:04:16.893
but we're showing what
happens when you have growth.

00:04:16.893 --> 00:04:19.370
And once again, what are
the drivers of growth?

00:04:19.370 --> 00:04:23.026
Well this could be the amount
of land that you have goes up.

00:04:23.026 --> 00:04:26.939
The amount of capital
that you have goes up.

00:04:26.939 --> 00:04:29.731
Capital could be things like factories,

00:04:29.731 --> 00:04:31.907
it could be machinery,

00:04:31.907 --> 00:04:36.079
you could have people, more
people are able to help produce

00:04:36.079 --> 00:04:38.032
the spoons or forks.

00:04:38.032 --> 00:04:40.723
You could just have better technology

00:04:40.723 --> 00:04:43.233
for producing spoons and forks.

00:04:43.233 --> 00:04:44.066
Sometimes people will even

00:04:44.066 --> 00:04:45.531
talk about entrepreneurial spirit,

00:04:45.531 --> 00:04:47.023
that people are able to
figure out better ways

00:04:47.023 --> 00:04:48.620
of combining these resources

00:04:48.620 --> 00:04:52.277
so that you could produce
more spoons or forks.

00:04:52.277 --> 00:04:54.703
But let's imagine now the other scenario.

00:04:54.703 --> 00:04:58.198
Let's imagine a scenario where Utenslandia

00:04:58.198 --> 00:05:00.948
gets into a war with Platelandia.

00:05:01.913 --> 00:05:05.625
And Platelandia sends their bombers in

00:05:05.625 --> 00:05:10.461
and starts destroying some of
the factories of Utenslandia

00:05:10.461 --> 00:05:12.583
and so what will happen in that situation?

00:05:12.583 --> 00:05:14.910
So before the war, this is that production

00:05:14.910 --> 00:05:18.121
possibilities curve for Utenslandia.

00:05:18.121 --> 00:05:21.715
But now, because of the
war, maybe Platelandia

00:05:21.715 --> 00:05:25.421
is able to take some
land from Utenslandia,

00:05:25.421 --> 00:05:29.609
maybe it's able to destroy
some of the factories

00:05:29.609 --> 00:05:31.254
and other forms of capital,

00:05:31.254 --> 00:05:35.257
maybe people flee Utenslandia
so there's less labor.

00:05:35.257 --> 00:05:37.199
And maybe for whatever reason,

00:05:37.199 --> 00:05:39.361
they can support less technology

00:05:39.361 --> 00:05:41.953
or they forget how to use
some of their technology

00:05:41.953 --> 00:05:44.867
'cause the war is so long and protracted.

00:05:44.867 --> 00:05:49.034
Well in that situation, your
PPC, you would see contraction.

00:05:50.190 --> 00:05:52.842
And contraction, I could depict it,

00:05:52.842 --> 00:05:56.225
let me shift my PPC, my
production possibilities curve

00:05:56.225 --> 00:05:58.058
inward just like this.

00:05:59.040 --> 00:06:02.939
So this is a situation where
we are seeing contraction.

00:06:02.939 --> 00:06:06.708
So big picture here, your
production possibilities curve

00:06:06.708 --> 00:06:08.221
is exactly what it says it is.

00:06:08.221 --> 00:06:12.162
It shows what can a, what
is the potential combination

00:06:12.162 --> 00:06:16.205
of, in this case, goods
that this nation can produce

00:06:16.205 --> 00:06:18.533
and if you're sitting on the curve,

00:06:18.533 --> 00:06:20.696
it shows that that nation, that country

00:06:20.696 --> 00:06:23.012
is efficiently using its resources.

00:06:23.012 --> 00:06:24.486
If you're sitting within the curve,

00:06:24.486 --> 00:06:26.578
it's inefficiently using its resources.

00:06:26.578 --> 00:06:28.570
And if you're on the right of the curve

00:06:28.570 --> 00:06:31.850
or beyond the curve,
well that's a situation

00:06:31.850 --> 00:06:34.225
where if you don't change the inputs,

00:06:34.225 --> 00:06:37.153
all else equal, this would
actually be unattainable.

00:06:37.153 --> 00:06:39.675
The way that you actually
do attain, get to points

00:06:39.675 --> 00:06:42.844
beyond the curve, is by
shifting the curve itself.

00:06:42.844 --> 00:06:45.538
By having more land,
more capital, more labor

00:06:45.538 --> 00:06:48.760
or more technology which we
see in this middle scenario.


Difference of functions

WEBVTT
Kind: captions
Language: en

00:00:00.159 --> 00:00:03.461
- [Instructor] We're told
that f of x is equal to two x

00:00:03.461 --> 00:00:06.249
times the square root of five minus four.

00:00:06.249 --> 00:00:09.577
And we're also told that g
of x is equal to x squared

00:00:09.577 --> 00:00:13.299
plus two x times the square
root of five minus one.

00:00:13.299 --> 00:00:16.524
And they want us to find g minus f

00:00:16.524 --> 00:00:17.535
of x.

00:00:17.535 --> 00:00:18.856
So pause this video,

00:00:18.856 --> 00:00:22.137
and see if you can work
through that on your own.

00:00:22.137 --> 00:00:25.606
So the key here is to just
realize what this notation means.

00:00:25.606 --> 00:00:26.773
G minus f of x

00:00:27.816 --> 00:00:30.066
is the same thing as g of x

00:00:31.884 --> 00:00:33.428
minus

00:00:33.428 --> 00:00:34.261
f of x.

00:00:35.191 --> 00:00:37.476
And so, again, if this was helpful to you,

00:00:37.476 --> 00:00:40.449
once again I encourage
you to pause the video.

00:00:40.449 --> 00:00:42.176
All right, now let's
work through this again.

00:00:42.176 --> 00:00:44.122
So this is going, or,
I guess the first time,

00:00:44.122 --> 00:00:45.171
but now that we know

00:00:45.171 --> 00:00:47.690
that this is equal to g of x minus f of x.

00:00:47.690 --> 00:00:48.996
So what is g of x?

00:00:48.996 --> 00:00:53.080
Well, that's the same thing
as x squared plus two x

00:00:53.080 --> 00:00:56.940
times the square root of five minus one.

00:00:56.940 --> 00:00:58.514
And what is f of x?

00:00:58.514 --> 00:01:01.485
Well, it's going to be two x

00:01:01.485 --> 00:01:04.407
times the square root of five minus four.

00:01:04.407 --> 00:01:07.150
And we are subtracting f of x from g of x.

00:01:07.150 --> 00:01:10.310
So let's subtract, this
is f of x, from g of x.

00:01:10.310 --> 00:01:11.248
And so now it's just going

00:01:11.248 --> 00:01:13.077
to be a little bit of
algebraic simplification.

00:01:13.077 --> 00:01:15.333
So this is going to be equal to,

00:01:15.333 --> 00:01:16.666
this is equal to

00:01:17.575 --> 00:01:21.573
x squared plus two x times
the square root of five

00:01:21.573 --> 00:01:22.705
minus one.

00:01:22.705 --> 00:01:26.011
And now we just have to
distribute this negative sign.

00:01:26.011 --> 00:01:28.282
So negative one times two x

00:01:28.282 --> 00:01:29.477
times the square root of five is,

00:01:29.477 --> 00:01:32.648
we're gonna have minus two x
times the square root of five.

00:01:32.648 --> 00:01:36.197
And then the negative of
negative four is positive four.

00:01:36.197 --> 00:01:38.407
Now let's see if we
can simplify this some.

00:01:38.407 --> 00:01:39.613
So this is going to be equal to,

00:01:39.613 --> 00:01:41.517
we only have one x squared term,

00:01:41.517 --> 00:01:42.808
so that's that one there.

00:01:42.808 --> 00:01:44.320
So we have x squared.

00:01:44.320 --> 00:01:47.007
Now let's see, we have two x
times the square root of five.

00:01:47.007 --> 00:01:48.365
And then we have another, oh,

00:01:48.365 --> 00:01:50.496
and then we subtract two x
times the square root of five.

00:01:50.496 --> 00:01:53.265
So these two cancel out with each other.

00:01:53.265 --> 00:01:54.701
So those cancel out.

00:01:54.701 --> 00:01:57.784
And then we have minus one plus four.

00:01:58.877 --> 00:02:02.198
So if we have negative one
and then we add four to it,

00:02:02.198 --> 00:02:03.956
we're going to have positive three.

00:02:03.956 --> 00:02:05.055
So if we just fact,

00:02:05.055 --> 00:02:07.602
if we take this and
this into consideration,

00:02:07.602 --> 00:02:10.381
four minus one is going
to be equal to three,

00:02:10.381 --> 00:02:11.290
and we're done.

00:02:11.290 --> 00:02:13.856
That's what g minus f of x is equal to,

00:02:13.856 --> 00:02:15.136
x squared plus three.


Proof of the derivative of sin(x)

WEBVTT
Kind: captions
Language: en

00:00:00.236 --> 00:00:01.671
- [Instructor] What we
have written here are two

00:00:01.671 --> 00:00:05.587
of the most useful derivatives
to know in calculus.

00:00:05.587 --> 00:00:07.722
If you know that the
derivative of sine of x

00:00:07.722 --> 00:00:09.683
with respect to x is cosine of x

00:00:09.683 --> 00:00:11.521
and the derivative of cosine of x

00:00:11.521 --> 00:00:14.824
with respect to x is negative sine of x,

00:00:14.824 --> 00:00:17.359
that can empower you to do many more,

00:00:17.359 --> 00:00:20.051
far more complicated derivatives.

00:00:20.051 --> 00:00:21.380
But what we're going to do in this video

00:00:21.380 --> 00:00:22.859
is dig a little bit deeper

00:00:22.859 --> 00:00:27.001
and actually prove this first derivative.

00:00:27.001 --> 00:00:28.319
I'm not gonna prove the second one.

00:00:28.319 --> 00:00:29.671
You can actually use it,

00:00:29.671 --> 00:00:32.357
using the information we're
going to do in this one,

00:00:32.357 --> 00:00:34.207
but it's just to make you feel good that

00:00:34.207 --> 00:00:35.917
someone's just not making this up,

00:00:35.917 --> 00:00:37.772
that there is a little bit of mathematical

00:00:37.772 --> 00:00:39.534
rigor behind it all.

00:00:39.534 --> 00:00:41.277
So let's try to calculate it.

00:00:41.277 --> 00:00:46.030
So the derivative with
respect to x of sine of x,

00:00:46.030 --> 00:00:49.115
by definition, this is
going to be the limit

00:00:49.115 --> 00:00:51.532
as delta x approaches zero

00:00:52.423 --> 00:00:54.028
of sine

00:00:54.028 --> 00:00:55.028
of x plus

00:00:56.123 --> 00:00:57.456
delta x minus

00:00:58.396 --> 00:00:59.229
sine of x,

00:01:00.302 --> 00:01:02.219
all of that over delta,

00:01:03.604 --> 00:01:05.487
all of that over delta x.

00:01:05.487 --> 00:01:09.046
This is really just the slope
of the line between the point

00:01:09.046 --> 00:01:12.650
x comma sine of x and x plus delta x

00:01:12.650 --> 00:01:16.118
comma sine of x plus delta x.

00:01:16.118 --> 00:01:19.080
So how can we evaluate this?

00:01:19.080 --> 00:01:23.561
Well, we can rewrite
sine of x plus delta x

00:01:23.561 --> 00:01:26.489
using our angle addition formulas

00:01:26.489 --> 00:01:29.181
that we learned during
our trig identities.

00:01:29.181 --> 00:01:31.440
So this is going to be the same thing

00:01:31.440 --> 00:01:33.139
as the limit

00:01:33.139 --> 00:01:35.639
as delta x approaches zero.

00:01:36.580 --> 00:01:40.747
I'll write, rewrite this using
our trig identity as cosine,

00:01:49.531 --> 00:01:50.364
as cosine

00:01:51.610 --> 00:01:52.995
of x

00:01:52.995 --> 00:01:53.828
times sine

00:01:55.029 --> 00:01:55.862
of delta x

00:01:57.074 --> 00:01:57.907
plus sine

00:01:59.264 --> 00:02:00.551
of x

00:02:00.551 --> 00:02:02.177
times cosine

00:02:02.177 --> 00:02:03.697
of delta x.

00:02:03.697 --> 00:02:07.000
And then we're going to
subtract this sine of x up here

00:02:07.000 --> 00:02:08.333
minus sine of x,

00:02:09.441 --> 00:02:11.016
all of that over,

00:02:11.016 --> 00:02:13.385
let me see if I can draw a
relatively straight line,

00:02:13.385 --> 00:02:14.718
all of that over

00:02:15.688 --> 00:02:17.308
delta x.

00:02:17.308 --> 00:02:21.269
So this can be rewritten
as being equal to the limit

00:02:21.269 --> 00:02:24.019
as delta x approaches zero of,

00:02:25.890 --> 00:02:28.390
let me write this part in red,

00:02:29.717 --> 00:02:32.550
so that would be cosine of x, sine

00:02:33.585 --> 00:02:35.268
of delta x,

00:02:35.268 --> 00:02:37.351
all of that over delta x.

00:02:38.566 --> 00:02:40.280
And then that's going to be plus,

00:02:40.280 --> 00:02:42.780
I'll do all of this in orange,

00:02:44.124 --> 00:02:45.057
all I'm doing is

00:02:45.057 --> 00:02:47.578
I have the sum of things
up here divided by delta x,

00:02:47.578 --> 00:02:51.816
I'm just breaking it up
a little bit, plus sine

00:02:51.816 --> 00:02:52.649
of x,

00:02:52.649 --> 00:02:54.892
cosine of delta x

00:02:54.892 --> 00:02:56.225
minus sine of x,

00:02:57.630 --> 00:03:00.530
all of that over delta x.

00:03:00.530 --> 00:03:01.954
And remember, I'm taking the limit

00:03:01.954 --> 00:03:04.033
of this entire expression.

00:03:04.033 --> 00:03:07.357
Well, the limit of a sum is
equal to the sum of the limits.

00:03:07.357 --> 00:03:10.056
So this is going to be equal to,

00:03:10.056 --> 00:03:11.943
I'll do this first part in red,

00:03:11.943 --> 00:03:13.040
the limit

00:03:13.040 --> 00:03:15.790
as delta x approaches zero of,

00:03:16.761 --> 00:03:20.344
let's see I can rewrite
this as cosine of x

00:03:21.357 --> 00:03:22.190
times sine

00:03:23.291 --> 00:03:24.957
of delta x

00:03:24.957 --> 00:03:25.957
over delta x

00:03:27.270 --> 00:03:28.103
plus

00:03:29.134 --> 00:03:30.521
the limit

00:03:30.521 --> 00:03:33.710
as delta x approaches zero

00:03:33.710 --> 00:03:37.230
of, and let's see I can
factor out a sine of x here.

00:03:37.230 --> 00:03:39.145
So it's times

00:03:39.145 --> 00:03:40.438
sine

00:03:40.438 --> 00:03:41.739
of x.

00:03:41.739 --> 00:03:42.979
I factor that out,

00:03:42.979 --> 00:03:45.824
and I'll be left with a cosine

00:03:45.824 --> 00:03:48.645
of delta x minus one,

00:03:48.645 --> 00:03:50.764
all of that over

00:03:50.764 --> 00:03:51.597
delta x.

00:03:52.724 --> 00:03:54.082
So that's this limit.

00:03:54.082 --> 00:03:56.959
And let's see if I can
simplify this even more.

00:03:56.959 --> 00:03:59.312
Let me scroll down a bit.

00:03:59.312 --> 00:04:02.028
So this left-hand
expression I can rewrite.

00:04:02.028 --> 00:04:04.167
This cosine of x has nothing to do with

00:04:04.167 --> 00:04:06.067
the limit as delta x approaches zero,

00:04:06.067 --> 00:04:08.760
so we can actually take
that outside of the limit.

00:04:08.760 --> 00:04:12.436
So we have the cosine of x times the limit

00:04:12.436 --> 00:04:15.386
as delta x approaches zero

00:04:15.386 --> 00:04:16.886
of sine of delta x

00:04:18.443 --> 00:04:19.526
over delta x.

00:04:20.867 --> 00:04:22.790
And now we need to add this thing,

00:04:22.790 --> 00:04:24.234
and let's see how I could write this.

00:04:24.234 --> 00:04:26.254
So I have a sine of x here.

00:04:26.254 --> 00:04:28.109
But actually, let me rewrite
this a little bit differently.

00:04:28.109 --> 00:04:30.383
Cosine of delta x minus one,

00:04:30.383 --> 00:04:34.550
that's the same thing as
one minus cosine of delta x

00:04:35.668 --> 00:04:37.937
times negative one.

00:04:37.937 --> 00:04:40.546
And so you have a sine of
x times a negative one.

00:04:40.546 --> 00:04:43.937
And since the delta x has
nothing to do with the sine of x,

00:04:43.937 --> 00:04:46.798
let me take that out, the
negative and the sine of x.

00:04:46.798 --> 00:04:48.965
So we have minus sine of x

00:04:50.255 --> 00:04:51.993
times the limit

00:04:51.993 --> 00:04:55.094
as delta x approaches zero of,

00:04:55.094 --> 00:04:59.961
what we have left over is
one minus cosine of delta x

00:04:59.961 --> 00:05:01.146
over

00:05:01.146 --> 00:05:01.979
delta x.

00:05:02.910 --> 00:05:04.216
Now, I'm not gonna do it in this video.

00:05:04.216 --> 00:05:06.575
In other videos, we will
actually do the proof.

00:05:06.575 --> 00:05:08.059
But in other videos we have shown,

00:05:08.059 --> 00:05:09.617
using the squeeze theorem,

00:05:09.617 --> 00:05:11.730
or sometimes known as
the sandwich theorem,

00:05:11.730 --> 00:05:13.914
that the limit is delta x approaches zero

00:05:13.914 --> 00:05:16.002
of sine of delta x over delta x,

00:05:16.002 --> 00:05:18.144
that this is equal to one.

00:05:18.144 --> 00:05:19.602
And we also show in another video,

00:05:19.602 --> 00:05:21.121
and that's based on the idea

00:05:21.121 --> 00:05:23.334
that this limit is equal to one,

00:05:23.334 --> 00:05:27.927
that this limit right over
here is equal to zero.

00:05:27.927 --> 00:05:30.194
And so what we are then left with,

00:05:30.194 --> 00:05:31.979
and I encourage you to watch the videos

00:05:31.979 --> 00:05:33.670
that prove this and this,

00:05:33.670 --> 00:05:35.247
although these are really useful limits

00:05:35.247 --> 00:05:37.102
to know in general in calculus,

00:05:37.102 --> 00:05:39.511
that what you're gonna be
left with is just cosine of x

00:05:39.511 --> 00:05:41.925
times one minus sine of x times zero.

00:05:41.925 --> 00:05:43.773
Well, all of this is just gonna go away,

00:05:43.773 --> 00:05:44.841
and you're gonna have,

00:05:44.841 --> 00:05:48.574
that is going to be equal to cosine of x.

00:05:48.574 --> 00:05:49.991
And you are done.


Endocrine system introduction

WEBVTT
Kind: captions
Language: en

00:00:00.273 --> 00:00:01.337
- [Instructor] What you
see in these pictures,

00:00:01.337 --> 00:00:03.823
this is a forward view
of a transparent man

00:00:03.823 --> 00:00:05.498
or a semitransparent man,

00:00:05.498 --> 00:00:07.602
and this is a posterior, or back view

00:00:07.602 --> 00:00:10.006
of a semitransparent woman.

00:00:10.006 --> 00:00:12.138
But what these organs that are depicted,

00:00:12.138 --> 00:00:15.550
these organs secrete molecules
into the bloodstream,

00:00:15.550 --> 00:00:17.791
and an organ that secretes things,

00:00:17.791 --> 00:00:20.368
these are called glands,

00:00:20.368 --> 00:00:23.358
and they secrete these
molecules into the blood stream

00:00:23.358 --> 00:00:25.738
that regulate other parts of the body,

00:00:25.738 --> 00:00:28.515
things that might be quite
far away from the organs,

00:00:28.515 --> 00:00:31.035
the glands that actually do the secretion.

00:00:31.035 --> 00:00:32.254
And so these molecules

00:00:32.254 --> 00:00:33.961
that regulate other parts of the body,

00:00:33.961 --> 00:00:35.985
these are called hormones.

00:00:35.985 --> 00:00:39.368
And the word hormone
comes from Greek hormōn,

00:00:39.368 --> 00:00:40.909
which means to set in motion,

00:00:40.909 --> 00:00:42.302
so one way to think about
it, these are molecules

00:00:42.302 --> 00:00:46.270
that set things in motion
in other parts of the body,

00:00:46.270 --> 00:00:48.233
and this is really to
regulate the body function.

00:00:48.233 --> 00:00:51.924
Now this entire system
of glands is referred to

00:00:51.924 --> 00:00:55.965
as the endocrine system,
endo- referring to fact that

00:00:55.965 --> 00:00:59.256
it's acting within the body,
-crine originally comes

00:00:59.256 --> 00:01:02.743
from Greek word to sift or
to differentiate something

00:01:02.743 --> 00:01:04.672
and it's a system of organs

00:01:04.672 --> 00:01:06.059
or I guess you could say glands

00:01:06.059 --> 00:01:07.703
that are secreting molecules,

00:01:07.703 --> 00:01:11.179
these hormones into the
bloodstream to regulate the body.

00:01:11.179 --> 00:01:12.690
I'm not going to go in-depth

00:01:12.690 --> 00:01:15.263
in all of these endocrine glands

00:01:15.263 --> 00:01:18.768
but just to give you an
appreciation of what they do

00:01:18.768 --> 00:01:20.766
and what these hormones are all about,

00:01:20.766 --> 00:01:23.143
we could list some of the more common ones

00:01:23.143 --> 00:01:24.741
that you might hear about.

00:01:24.741 --> 00:01:29.550
So for example, the thyroid
gland produces thyroid hormone.

00:01:29.550 --> 00:01:31.862
This is a version of thyroid hormone.

00:01:31.862 --> 00:01:33.975
You see your carbons in the dark gray,

00:01:33.975 --> 00:01:35.926
your hydrogens in the white.

00:01:35.926 --> 00:01:38.988
You see your oxygens in
the red, nitrogen in blue,

00:01:38.988 --> 00:01:42.386
and these big atoms right
over here, these are iodine,

00:01:42.386 --> 00:01:44.763
and thyroid hormone
plays an important role

00:01:44.763 --> 00:01:45.995
in your metabolism.

00:01:45.995 --> 00:01:48.176
In fact, if you have too
much thyroid hormone,

00:01:48.176 --> 00:01:51.386
that's a disorder called hyperthyroidism,

00:01:51.386 --> 00:01:53.784
which would make your
metabolism overactive.

00:01:53.784 --> 00:01:56.784
Likewise, if you have too
little thyroid hormone,

00:01:56.784 --> 00:02:00.153
that's a disorder known as hypothyroidism,

00:02:00.153 --> 00:02:03.699
in which case your metabolism
isn't active enough.

00:02:03.699 --> 00:02:07.054
You have hormones like adrenaline

00:02:07.054 --> 00:02:09.567
that are released by the adrenal glands,

00:02:09.567 --> 00:02:11.887
and that's where it gets
the word adrenaline from.

00:02:11.887 --> 00:02:14.106
It's often known as epinephrine,

00:02:14.106 --> 00:02:16.440
and adrenaline, you
might hear things like,

00:02:16.440 --> 00:02:18.403
"Hey, so and so is an adrenaline junkie,"

00:02:18.403 --> 00:02:20.188
which means they really like a thrill,

00:02:20.188 --> 00:02:22.444
and adrenaline actually
does play a role there.

00:02:22.444 --> 00:02:24.468
It's involved in the
fight-or-flight response,

00:02:24.468 --> 00:02:26.162
where it'll increase your heart rate

00:02:26.162 --> 00:02:28.356
and increase blood flow to the muscles.

00:02:28.356 --> 00:02:30.411
And what's really interesting
about all of these hormones

00:02:30.411 --> 00:02:32.636
is they have so many impacts on the body

00:02:32.636 --> 00:02:34.556
because they're released
into the bloodstream

00:02:34.556 --> 00:02:39.096
and to different cells they
might do different things.

00:02:39.096 --> 00:02:41.766
This right over here is
a variation of estrogen,

00:02:41.766 --> 00:02:45.243
which is produced primarily
in females in the ovaries,

00:02:45.243 --> 00:02:47.299
but it also exists in a male body

00:02:47.299 --> 00:02:50.939
and it's associated with a
lot of female bodily function,

00:02:50.939 --> 00:02:52.815
but once again, not strictly female.

00:02:52.815 --> 00:02:55.141
Estrogen also exists in males.

00:02:55.141 --> 00:02:58.009
Similarly, you have testosterone,

00:02:58.009 --> 00:03:00.983
which is associated with male function

00:03:00.983 --> 00:03:03.299
but it also exists in females,

00:03:03.299 --> 00:03:06.285
and it's primarily produced
in men in the testes.

00:03:06.285 --> 00:03:08.175
Thus the name testosterone,

00:03:08.175 --> 00:03:10.957
but it can also be produced
by the adrenal glands.

00:03:10.957 --> 00:03:14.451
And women, it can be
produced by the ovaries.

00:03:14.451 --> 00:03:16.384
But you could also have
a molecule like insulin

00:03:16.384 --> 00:03:19.035
which you can see is much
larger than the other hormones

00:03:19.035 --> 00:03:20.193
that we have looked at.

00:03:20.193 --> 00:03:21.686
It's produced in the pancreas

00:03:21.686 --> 00:03:23.502
and it plays a super-important role

00:03:23.502 --> 00:03:26.367
in how we process sugars
and how we store fat

00:03:26.367 --> 00:03:29.227
and scientists are constantly
discovering new roles

00:03:29.227 --> 00:03:31.774
for these various hormones.

00:03:31.774 --> 00:03:35.279
Insulin in particular you
might associate with diabetes.

00:03:35.279 --> 00:03:38.201
People with Type 1 diabetes
aren't able to produce

00:03:38.201 --> 00:03:40.995
enough insulin to take the
sugar out of their blood stream,

00:03:40.995 --> 00:03:42.834
to have the cells absorb the sugar.

00:03:42.834 --> 00:03:44.957
Insulin will bind to the surface of a cell

00:03:44.957 --> 00:03:47.029
so that it will start taking in sugar

00:03:47.029 --> 00:03:48.475
from the blood stream.

00:03:48.475 --> 00:03:52.241
People with Type 2 diabetes,
they have an insensitivity

00:03:52.241 --> 00:03:54.752
to insulin, so they might
have to take extra insulin

00:03:54.752 --> 00:03:57.862
in order for their cells to
take in the proper amount

00:03:57.862 --> 00:03:58.976
of sugar.

00:03:58.976 --> 00:04:01.140
But the big idea here is
that the endocrine system,

00:04:01.140 --> 00:04:03.271
although it might not be as obvious,

00:04:03.271 --> 00:04:04.889
or it might not be as well known

00:04:04.889 --> 00:04:06.961
as something like say the nervous system,

00:04:06.961 --> 00:04:09.565
it plays a pivotal role in your body.

00:04:09.565 --> 00:04:11.237
It helps regulate your body.

00:04:11.237 --> 00:04:13.344
It helps keep it at the right temperature,

00:04:13.344 --> 00:04:14.973
the right blood pressure,

00:04:14.973 --> 00:04:16.666
your heart pumping at the right rate.

00:04:16.666 --> 00:04:18.021
One way to think about this is

00:04:18.021 --> 00:04:21.487
the notion of homeostasis, which is

00:04:21.487 --> 00:04:24.987
derived from similar and staying the same.

00:04:25.900 --> 00:04:27.837
So keeping your body at
the right temperature

00:04:27.837 --> 00:04:29.679
regardless of what the
temperature is outside

00:04:29.679 --> 00:04:31.400
or regardless of what your body is doing,

00:04:31.400 --> 00:04:34.633
there's a whole series of
roles that these hormones,

00:04:34.633 --> 00:04:36.968
which are released by
these endocrine glands

00:04:36.968 --> 00:04:37.968
actually do.