4 Economists

WEBVTT
Kind: captions
Language: en

00:00:00.639 --> 00:00:01.779
- [Voiceover] Many economists believe

00:00:01.779 --> 00:00:03.203
that since resources are scarce

00:00:03.203 --> 00:00:06.259
and since human desires
cannot all be blank,

00:00:06.259 --> 00:00:10.592
a method of blank is needed.

00:00:10.592 --> 00:00:11.822
So, let's see.

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So let's look at the first choice.

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Many economists believe that
since resources are scarce.

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So there's only so many resources.

00:00:17.479 --> 00:00:19.665
We don't have an infinite
amount of resources.

00:00:19.665 --> 00:00:23.766
And since human desires
cannot all be indulged,

00:00:23.766 --> 00:00:27.534
a method of apportionment is needed.

00:00:27.534 --> 00:00:29.380
That actually feels pretty good.

00:00:29.380 --> 00:00:33.163
To indulge means to kind of allow yourself

00:00:33.163 --> 00:00:34.688
or allow someone else
to have the pleasure,

00:00:34.688 --> 00:00:36.946
any pleasure that they want.

00:00:36.946 --> 00:00:40.919
And so, you can't indulge
all human desires.

00:00:40.919 --> 00:00:43.339
That means allowing everyone
to do anything they want,

00:00:43.339 --> 00:00:45.202
use as many resources as they want.

00:00:45.202 --> 00:00:47.999
We cannot do that, because
we have scarce resources.

00:00:47.999 --> 00:00:50.151
So indulge is feeling pretty good.

00:00:50.151 --> 00:00:52.259
A method of apportionment is needed.

00:00:52.259 --> 00:00:53.791
Well that also makes sense.

00:00:53.791 --> 00:00:56.239
You can't indulge everybody.

00:00:56.239 --> 00:00:58.300
You only have so many resources.

00:00:58.300 --> 00:01:00.920
So we need some way to
split those resources,

00:01:00.920 --> 00:01:04.260
to apportion those
resources amongst people,

00:01:04.260 --> 00:01:05.639
and so this one actually feels,

00:01:05.639 --> 00:01:09.253
this one is feeling pretty good,

00:01:09.253 --> 00:01:12.856
but let's just verify,
I just used this word,

00:01:12.856 --> 00:01:16.239
that these other choices right
over here aren't as good.

00:01:16.239 --> 00:01:17.981
So since many economists believe

00:01:17.981 --> 00:01:19.479
that since resources are scarce

00:01:19.479 --> 00:01:23.603
and since human desires
cannot all be verified.

00:01:23.603 --> 00:01:25.379
So verified means validating,

00:01:25.379 --> 00:01:29.265
proving that someone has some desire,

00:01:29.265 --> 00:01:30.639
so that's already feeling weird.

00:01:30.639 --> 00:01:32.703
A method of distribution is needed.

00:01:32.703 --> 00:01:35.618
So distribution isn't
bad for the second one,

00:01:35.618 --> 00:01:37.679
but verifying human desires.

00:01:37.679 --> 00:01:39.368
This one feels a little bit off.

00:01:39.368 --> 00:01:42.669
And remember, we always want
to pick the best choice.

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And so, A is definitely
a much better choice.

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We're not talking about verifying,

00:01:46.950 --> 00:01:49.840
making sure that we know
the actual human desires

00:01:49.840 --> 00:01:53.710
and then distributing based on it.

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I would rule this one right over here,

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this one right over
here seems a little off.

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Since human desires cannot all be usurped.

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That means you're kind of ignoring them

00:02:10.793 --> 00:02:14.498
and removing them and putting in place

00:02:14.498 --> 00:02:16.658
different desires somehow.

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A method of expropriation.

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So that's kind of taking from someone.

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A method of kind of
expropriation is needed.

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So once again, we're not talking about

00:02:25.334 --> 00:02:28.679
trying to usurp folks' desires

00:02:28.679 --> 00:02:31.760
nor kind of a method of
taking things from folks.

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So once again, this
one feels very strange.

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And since human desires
cannot all be expressed,

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a method of reparation is needed.

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So it is true, not all human
desires can be expressed,

00:02:43.258 --> 00:02:45.398
but that doesn't seem
to be a counterbalance

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to the whole notion of
resources being scarce.

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So this one already feels weird.

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And a method of reparation.

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Reparations are essentially
a payment to someone

00:02:56.156 --> 00:02:58.292
because of injustices
that you've done to them.

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And so, we're not really talking about

00:02:59.820 --> 00:03:01.048
justice and injustice right over here.

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So once again, this also feels weird

00:03:03.069 --> 00:03:05.760
and nowhere near as good as choice A.

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Since human desires
cannot all be anticipated,

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that's true, a method of advertising.

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So advertising, once again
we're not talking about

00:03:13.000 --> 00:03:15.987
how do we communicate with people,

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what they may or may not want,

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or how do we convince people
what they may or may not want.

00:03:19.808 --> 00:03:22.200
We're going against the idea of

00:03:22.200 --> 00:03:24.020
hey, we only have so many resources,

00:03:24.020 --> 00:03:26.313
and we can't give everything to everyone,

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so we need some way of divvying
up those scarce resources.

00:03:29.196 --> 00:03:30.401
So once again, the advertising

00:03:30.401 --> 00:03:33.841
really seems a little bit off.


3 Camouflage

WEBVTT
Kind: captions
Language: en

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- [Voiceover] Nightjars
possess a camouflage

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perhaps unparalleled in the bird world.

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So I guess nightjars are birds.

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By day they roost hidden in shady woods,

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so blank with their
surroundings that they are

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nearly impossible to blank.

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So before I even looked at the choices,

00:00:17.181 --> 00:00:21.321
they're telling us that these
nightjars, which are birds,

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they have a camouflage
unparalleled in the bird world.

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So they're really good mixing
in with their background.

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That's what camouflage means.

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By day they roost hidden
in shady woods, so--

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And so, I would say something like

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so mixed with their surroundings

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or maybe so blended
with their surroundings.

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I'm not even looking at the choices yet.

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So mixed or blended
with their surroundings

00:00:42.137 --> 00:00:44.337
that they are nearly impossible to maybe

00:00:44.337 --> 00:00:49.337
find or pick out, find or pick out,

00:00:49.507 --> 00:00:51.964
or maybe even impossible to

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or they are nearly impossible to see.

00:00:54.344 --> 00:00:55.824
So those are the types of words

00:00:55.824 --> 00:00:58.196
that I would try to look
for for these blanks.

00:00:58.196 --> 00:01:00.227
And now let's look at the choices.

00:01:00.227 --> 00:01:04.187
So this first choice, so
vexed with their surroundings

00:01:04.187 --> 00:01:06.927
that they are nearly
impossible to dislodge.

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So to be vexed with your--

00:01:09.787 --> 00:01:11.691
So that's kind of angry or annoyed

00:01:11.691 --> 00:01:15.077
or kind of worried or frustrated
with your surroundings.

00:01:15.077 --> 00:01:16.807
Now that doesn't make a lot of sense,

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that the birds would be that way

00:01:18.247 --> 00:01:19.096
regarding their surroundings.

00:01:19.096 --> 00:01:21.807
So this is already starting to feel weird.

00:01:21.807 --> 00:01:23.867
And so vexed with their surroundings

00:01:23.867 --> 00:01:26.108
that they are nearly
impossible to dislodge.

00:01:26.108 --> 00:01:27.447
Well that means that they're kind of

00:01:27.447 --> 00:01:28.717
so stuck into their surroundings

00:01:28.717 --> 00:01:30.548
that you can't even pull
them out, if you wanted to.

00:01:30.548 --> 00:01:33.240
So this one is feeling very wrong.

00:01:33.240 --> 00:01:34.547
Let's read the next one.

00:01:34.547 --> 00:01:36.508
So blended with their surroundings,

00:01:36.508 --> 00:01:38.645
and that's actually the
actual word that I picked out,

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so blended with their surroundings

00:01:40.748 --> 00:01:43.799
that they are nearly
impossible to discern.

00:01:43.799 --> 00:01:45.680
Well, discern really means to be able to

00:01:45.680 --> 00:01:47.707
kind of pick something
out of its background,

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to see it out of its background.

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So it's very similar in meaning

00:01:50.491 --> 00:01:53.059
to the words that I wanted to pick as is.

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So this looks like the
choice that I would go.

00:01:55.863 --> 00:01:57.607
This looks already like the best choice,

00:01:57.607 --> 00:01:58.507
and we could read it.

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Nightjars possess a camouflage

00:01:59.905 --> 00:02:02.567
perhaps unparalleled in the bird world.

00:02:02.567 --> 00:02:04.957
By day they roost hidden in shady woods,

00:02:04.957 --> 00:02:08.027
so blended with their surroundings

00:02:08.027 --> 00:02:11.236
that they are nearly
impossible to discern.

00:02:11.236 --> 00:02:13.387
So that makes a lot of sense.

00:02:13.387 --> 00:02:17.448
But let's verify that these
other ones aren't as good.

00:02:17.448 --> 00:02:20.039
So, so harmonized with their surroundings

00:02:20.039 --> 00:02:23.307
that they are nearly
impossible to interrupt.

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So harmonize isn't a horrible word here.

00:02:26.427 --> 00:02:28.947
It kind of means in sync with something.

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So maybe they're harmonized
with their surroundings,

00:02:32.054 --> 00:02:34.194
but nearly impossible to interrupt.

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What are we interrupting them doing?

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The interrupt especially is
what really makes choice C

00:02:39.007 --> 00:02:41.433
really not appropriate.

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So impatient with their surroundings.

00:02:43.180 --> 00:02:44.470
So that already doesn't make sense.

00:02:44.470 --> 00:02:46.334
I don't even have to read the rest of it.

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So we could rule that out.

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Distinguish actually isn't a
bad word for the second blank.

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That they are nearly
impossible to distinguish.

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That kind of has the same
type of meaning as discern

00:02:55.727 --> 00:02:59.496
or pick out or see,
relative to its background,

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but this impatient was
weird for this first blank.

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So impatient with their surroundings?

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That doesn't sound like how
we would talk about a bird,

00:03:07.727 --> 00:03:09.753
a bird being impatient
with its surroundings.

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So integrated with its surroundings.

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So that's not bad.

00:03:14.947 --> 00:03:16.514
That's kind of like
being mixed or blended.

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Being integrated means kind
of so part of the surroundings

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that they are nearly
impossible to classify.

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So classifying something means
you're really kind of seeing.

00:03:25.734 --> 00:03:27.307
You're putting a label on it.

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You're trying to see how it's different

00:03:28.459 --> 00:03:31.043
or similar to other things.

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It's kind of like, it
has some connection to

00:03:34.581 --> 00:03:37.947
being able to see something
or discern or find something,

00:03:37.947 --> 00:03:38.747
but it goes further.

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You're not only discerning
it or seeing it,

00:03:40.407 --> 00:03:42.085
you're trying to kind
of put it into a bucket.

00:03:42.085 --> 00:03:43.877
You're trying to classify it.

00:03:43.877 --> 00:03:47.038
So if I didn't have choice B here,

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maybe I could somewhat argue for choice E,

00:03:49.847 --> 00:03:51.067
but the key to realize is

00:03:51.067 --> 00:03:52.406
you need to pick the best choice.

00:03:52.406 --> 00:03:56.547
So E is kind of a not horrible choice.

00:03:56.547 --> 00:03:57.962
It's still a little bit strange,

00:03:57.962 --> 00:03:59.670
but B is way, way better.

00:03:59.670 --> 00:04:02.907
So we could rule out E as well.


2 Defying oppression

WEBVTT
Kind: captions
Language: en

00:00:00.894 --> 00:00:02.094
- [Voiceover] One of the characters

00:00:02.094 --> 00:00:06.397
in Milton Murayama's
novel is considered blank

00:00:06.397 --> 00:00:09.540
because he deliberately defies

00:00:09.540 --> 00:00:12.965
an oppressive hierarchical society.

00:00:12.965 --> 00:00:14.512
So we can think about what word (mumbles)

00:00:14.512 --> 00:00:18.075
you'd be considered blank, if
you're deliberately defying

00:00:18.075 --> 00:00:21.516
an oppressive hierarchical society.

00:00:21.516 --> 00:00:25.134
So let's think about it, so
the first choice is rebellious.

00:00:25.134 --> 00:00:28.207
Well this seems pretty good, rebellious...

00:00:28.207 --> 00:00:29.669
if you're rebellious,
that means that you're

00:00:29.669 --> 00:00:32.795
rebelling against something,
that you tend to rebel.

00:00:32.795 --> 00:00:35.872
To rebel means that
you're fighting the power,

00:00:35.872 --> 00:00:38.806
you are rising up against the man.

00:00:38.806 --> 00:00:42.547
You are deliberately defying an oppressive

00:00:42.547 --> 00:00:46.069
hierarchical society, so this
seems to be a pretty good fit.

00:00:46.069 --> 00:00:49.373
One of the characters in
Milton Murayama's novel

00:00:49.373 --> 00:00:53.367
is considered rebellious,
because he rebels against

00:00:53.367 --> 00:00:55.166
an oppressive hierarchical society.

00:00:55.166 --> 00:00:58.542
He deliberately defies an
oppressive hierarchical society.

00:00:58.542 --> 00:01:02.944
You could literally replace
the word, he deliberately...

00:01:02.944 --> 00:01:07.066
You could replace the word
defies with the word rebel,

00:01:07.066 --> 00:01:08.633
and it would make complete sense,

00:01:08.633 --> 00:01:10.797
because he deliberately rebels...

00:01:10.797 --> 00:01:13.973
rebels against...

00:01:14.373 --> 00:01:18.863
rebels against an oppressive
hierarchical society.

00:01:18.863 --> 00:01:21.444
So, someone who defies, or rebels against,

00:01:21.444 --> 00:01:22.907
well, they're rebellious, but we can look

00:01:22.907 --> 00:01:24.644
at these other choices to just make sure

00:01:24.644 --> 00:01:27.288
that they don't also fit in some way.

00:01:27.288 --> 00:01:28.498
So here they're saying...

00:01:28.498 --> 00:01:31.157
so choice B would be,
one of the characters in

00:01:31.157 --> 00:01:34.523
Milton Murayama's novel
is considered impulsive.

00:01:34.523 --> 00:01:36.395
Well impulsive just means that

00:01:36.395 --> 00:01:39.851
you don't think before you
act, you just do something.

00:01:39.851 --> 00:01:41.884
You could be impulsive in
a lot of different ways,

00:01:41.884 --> 00:01:43.938
it could be, in some ways,
rebelling, but it could

00:01:43.938 --> 00:01:48.424
be impulsive, just not acting
before you're thinking.

00:01:48.424 --> 00:01:51.208
So this doesn't seem as close to

00:01:51.208 --> 00:01:54.839
deliberately defying an
oppressive hierarchical society.

00:01:54.839 --> 00:01:58.167
Artistic, well that doesn't
really, that's not even,

00:01:58.167 --> 00:02:00.841
deliberately defying an
oppressive hierarchical society.

00:02:00.841 --> 00:02:04.138
Sometimes artists have done
things like that, but rebelling,

00:02:04.138 --> 00:02:06.216
or being rebellious is much closer to this

00:02:06.216 --> 00:02:08.178
than just being artistic,
you could be artistic

00:02:08.178 --> 00:02:11.085
and have nothing to do with defying

00:02:11.085 --> 00:02:12.528
an oppressive hierarchical society.

00:02:12.528 --> 00:02:15.759
You'd just wanna go into a
field and work on your art.

00:02:15.759 --> 00:02:19.922
Industrious, well
industrious means you're...

00:02:19.922 --> 00:02:22.558
you're always busy doing
things, you're productive,

00:02:22.558 --> 00:02:26.172
you're working hard, and
someone who's rebellious

00:02:26.172 --> 00:02:28.610
might be industrious in their rebellion,

00:02:28.610 --> 00:02:31.419
but it doesn't mean that
you're deliberately defying

00:02:31.419 --> 00:02:33.590
an oppressive hierarchical society.

00:02:33.590 --> 00:02:35.958
So, if anything, you
could be very industrious

00:02:35.958 --> 00:02:38.350
being a part of the oppressive
hierarchical society,

00:02:38.350 --> 00:02:41.488
you're busy oppressing people. (laughs)

00:02:41.488 --> 00:02:44.537
So we'll rule that out, and then,

00:02:44.537 --> 00:02:46.242
it's considered tyrannical, because

00:02:46.242 --> 00:02:49.278
he deliberately defies an
oppressive hierarchical society.

00:02:49.278 --> 00:02:52.569
So tyrannical, you see the...

00:02:52.569 --> 00:02:55.437
root of tyrant right over
there, so that's really...

00:02:55.437 --> 00:02:59.091
you're being like a tyrant.

00:02:59.091 --> 00:03:02.694
And so, someone who's rebelling
against, or who's defying

00:03:02.694 --> 00:03:03.936
an oppressive hierarchical society,

00:03:03.936 --> 00:03:06.258
that's kind of the opposite of a tyrant.

00:03:06.258 --> 00:03:08.405
A tyrant is someone who would run

00:03:08.405 --> 00:03:10.588
the oppressive hierarchical society.

00:03:10.588 --> 00:03:12.536
So I would rule that one out, as well,

00:03:12.536 --> 00:03:13.766
so we can feel even better.

00:03:13.766 --> 00:03:15.914
But if I was doing this
under time-pressure,

00:03:15.914 --> 00:03:18.634
I got to rebellious, that feels right,

00:03:18.634 --> 00:03:22.708
you're rebelling against
the hierarchical society.

00:03:22.708 --> 00:03:24.945
I would just go with that and move on,

00:03:24.945 --> 00:03:27.026
and if you have some extra
time, you could come back

00:03:27.026 --> 00:03:29.622
and review these other choices.


1 Private universities

WEBVTT
Kind: captions
Language: en

00:00:00.541 --> 00:00:04.994
- Many private universities
depend heavily on blank,

00:00:04.994 --> 00:00:07.977
the wealthy individuals who support them

00:00:07.977 --> 00:00:10.548
with gifts and bequests.

00:00:10.548 --> 00:00:12.941
So whatever blank is,
they're kind of saying

00:00:12.941 --> 00:00:15.231
well, another way of
describing blank is that

00:00:15.231 --> 00:00:17.944
they're the wealthy
individuals who support them

00:00:17.944 --> 00:00:19.556
with gifts and bequests.

00:00:19.556 --> 00:00:21.824
So which of these words are the best

00:00:21.824 --> 00:00:24.264
or best represent wealthy individuals

00:00:24.264 --> 00:00:26.824
who would support a private university

00:00:26.824 --> 00:00:28.944
with gifts and bequests?

00:00:28.944 --> 00:00:30.984
So the instructors, they
would teach at the university,

00:00:30.984 --> 00:00:33.227
but they don't tend to be wealthy,

00:00:33.227 --> 00:00:36.684
and they don't tend to
be giving large gifts

00:00:36.684 --> 00:00:37.828
or even be giving gifts at all.

00:00:37.828 --> 00:00:39.413
They take a salary from the university.

00:00:39.413 --> 00:00:42.754
So I would rule out the instructors.

00:00:42.754 --> 00:00:44.624
The administrators, well
these are the people

00:00:44.624 --> 00:00:47.604
who kind of run the
university, but once again,

00:00:47.604 --> 00:00:49.239
they don't tend to be wealthy,

00:00:49.239 --> 00:00:51.984
and they don't tend to give
gifts to the university,

00:00:51.984 --> 00:00:53.273
donate money to the university.

00:00:53.273 --> 00:00:56.340
So I will rule that out.

00:00:56.340 --> 00:00:58.369
Monitors, well the monitor is
something that would mean to

00:00:58.369 --> 00:01:01.880
kind of observe something,
see what's going on.

00:01:01.880 --> 00:01:04.740
That doesn't really mean
giving to something.

00:01:04.740 --> 00:01:07.380
So I would rule that out.

00:01:07.380 --> 00:01:09.360
Accountants, well these are the people

00:01:09.360 --> 00:01:10.320
who take account of things.

00:01:10.320 --> 00:01:13.280
They're the ones who kind
of keep track of the books,

00:01:13.280 --> 00:01:17.760
who keep track of the
money for any organization,

00:01:17.760 --> 00:01:19.413
in this case maybe
university, but once again,

00:01:19.413 --> 00:01:21.020
they're not the wealthy individuals

00:01:21.020 --> 00:01:23.465
who would support the university
with gifts and bequests.

00:01:23.465 --> 00:01:25.180
So I'd rule those out.

00:01:25.180 --> 00:01:27.340
So, I've ruled out all the choices,

00:01:27.340 --> 00:01:30.360
so we should hope that it's
going to be benefactors,

00:01:30.360 --> 00:01:32.820
and benefactors makes
sense, because notice,

00:01:32.820 --> 00:01:36.521
it has the word bene.

00:01:36.521 --> 00:01:38.420
Well, you don't see
exactly the word benefit.

00:01:38.420 --> 00:01:39.840
You see the word benefact,

00:01:39.840 --> 00:01:42.020
but it's really coming
from the word benefit,

00:01:42.020 --> 00:01:44.080
and if you're benefiting someone,

00:01:44.080 --> 00:01:45.721
that means you're doing
something for them.

00:01:45.721 --> 00:01:48.320
So a benefactor is someone
who's doing something

00:01:48.320 --> 00:01:52.307
for, in this case, a private university.

00:01:52.307 --> 00:01:54.640
So I would definitely go with benefactors,

00:01:54.640 --> 00:01:56.020
and you could put it back in the sentence

00:01:56.020 --> 00:01:58.790
and see that it actually
sounds quite right.

00:01:58.790 --> 00:02:02.781
Many private universities
depend heavily on benefactors,

00:02:02.781 --> 00:02:04.999
the wealthy individuals who support them

00:02:04.999 --> 00:02:06.740
with gifts and bequests.

00:02:06.740 --> 00:02:08.661
You could almost say,
many private universities

00:02:08.661 --> 00:02:10.563
depend heavily on benefactors,

00:02:10.563 --> 00:02:13.261
the wealthy individuals who benefit them

00:02:13.261 --> 00:02:15.940
with gifts and bequests.


Analyzing event probability for independence

WEBVTT
Kind: captions
Language: en

00:00:00.472 --> 00:00:02.175
Voiceover:Tomas's favorite colors,

00:00:02.175 --> 00:00:05.994
Tomas's favorite colors
are blue and green.

00:00:05.994 --> 00:00:08.189
He has one blue shirt, one green shirt,

00:00:08.189 --> 00:00:10.951
one blue hat, one green scarf,

00:00:10.951 --> 00:00:13.800
one blue pair of pants,

00:00:13.800 --> 00:00:16.290
and one green pair of pants.

00:00:16.290 --> 00:00:19.753
Tomas selects one of
these garments at random.

00:00:19.753 --> 00:00:23.209
Let A be the event that
he selects a blue garment.

00:00:23.209 --> 00:00:28.630
Let B be the event that
he chooses a shirt.

00:00:28.630 --> 00:00:30.338
Which of the following
statements are true?

00:00:30.338 --> 00:00:31.373
And they all, let's see,

00:00:31.373 --> 00:00:32.173
and before I even read them,

00:00:32.173 --> 00:00:35.371
they all deal with the
probability of event A

00:00:35.371 --> 00:00:36.682
probability of event B,

00:00:36.682 --> 00:00:37.908
probability of B given A,

00:00:37.908 --> 00:00:39.261
probability of A given B,

00:00:39.261 --> 00:00:41.182
probability of A and B.

00:00:41.182 --> 00:00:44.319
So actually let's just calculate
these things ahead of time

00:00:44.319 --> 00:00:46.959
before we even look at
these right over here.

00:00:46.959 --> 00:00:49.562
So let's just think about,
let's just think about

00:00:49.562 --> 00:00:52.264
probability of A.

00:00:52.264 --> 00:00:54.462
The probability of A.

00:00:54.462 --> 00:00:57.610
That's the probability
that he picks a blue,

00:00:57.610 --> 00:01:00.740
he selects a blue garment.

00:01:00.740 --> 00:01:02.254
So how many equally
likely outcomes are there?

00:01:02.254 --> 00:01:06.133
Well, there's one, two,
three, four, five, six

00:01:06.133 --> 00:01:07.471
equally likely outcomes.

00:01:07.471 --> 00:01:10.748
And how many involve
selecting a blue garment?

00:01:10.748 --> 00:01:14.180
Well, there's one, two, three

00:01:14.180 --> 00:01:15.302
of the equally likely outcomes

00:01:15.302 --> 00:01:17.341
involve selecting a blue garment.

00:01:17.341 --> 00:01:20.471
So he has a 3/6 or 1/2 probability

00:01:20.471 --> 00:01:22.426
of selecting a blue garment.

00:01:22.426 --> 00:01:24.376
So what's the probability of B?

00:01:24.376 --> 00:01:27.117
What's the probability of B?

00:01:27.117 --> 00:01:28.751
And I'll use neutral colors

00:01:28.751 --> 00:01:30.595
since we're just saying he's B

00:01:30.595 --> 00:01:33.304
the event that he chooses a shirt.

00:01:33.304 --> 00:01:36.313
So once again, there's six possible items

00:01:36.313 --> 00:01:38.395
equally likely outcomes here,

00:01:38.395 --> 00:01:39.684
and which involve a shirt.

00:01:39.684 --> 00:01:44.822
Well, there's one, there's two,

00:01:44.822 --> 00:01:46.338
so it looks like two of the six

00:01:46.338 --> 00:01:47.929
involve picking a shirt.

00:01:47.929 --> 00:01:52.340
Or we could say the probability
of B is equal to 1/3.

00:01:52.340 --> 00:01:56.739
Now what's the probability of A given B?

00:01:56.739 --> 00:01:58.242
Let's write that down.

00:01:58.242 --> 00:02:00.458
What's the probability of

00:02:00.458 --> 00:02:01.641
let's use a new color,

00:02:01.641 --> 00:02:08.453
What's the probability of A given B?

00:02:08.453 --> 00:02:10.400
I'll do those in the colors.

00:02:10.400 --> 00:02:12.969
A given that B has happened.

00:02:12.969 --> 00:02:14.108
So this is saying

00:02:14.108 --> 00:02:19.569
what's the probability of A given B?

00:02:19.569 --> 00:02:21.800
The probability of A given B

00:02:21.800 --> 00:02:23.307
is the probability that
he picks a blue garment

00:02:23.307 --> 00:02:26.891
given that he has picked a shirt.

00:02:26.891 --> 00:02:31.940
So, this the given B that
restricts our outcomes

00:02:31.940 --> 00:02:32.953
to these two.

00:02:32.953 --> 00:02:35.980
So the probability that
he picks a blue item

00:02:35.980 --> 00:02:39.225
well, that's one out of the
two equally likely ones.

00:02:39.225 --> 00:02:41.266
So that is a 1/2 probability

00:02:41.266 --> 00:02:46.680
that he picks a blue garment

00:02:46.680 --> 00:02:47.801
given that he's picked a shirt,

00:02:47.801 --> 00:02:49.980
and that's because there is one blue shirt

00:02:49.980 --> 00:02:50.613
and one green shirt.

00:02:50.613 --> 00:02:53.210
Let's look at the
probability of B given A.

00:02:53.210 --> 00:02:58.145
Probability of B given A.

00:02:58.145 --> 00:03:03.338
B given, probability of B given A.

00:03:03.338 --> 00:03:06.952
So assuming we have picked a blue garment.

00:03:06.952 --> 00:03:09.800
So assuming we've picked a blue garment.

00:03:09.800 --> 00:03:13.485
So it's either that one or that one.

00:03:13.624 --> 00:03:15.117
What's the probability that we have also,

00:03:15.117 --> 00:03:19.581
What's the probability that
we have also chosen a shirt?

00:03:19.581 --> 00:03:23.232
Well, there's one, two,
three possibilities,

00:03:23.232 --> 00:03:24.628
equally likely possibilities

00:03:24.628 --> 00:03:26.165
that we have a blue garment.

00:03:26.165 --> 00:03:29.570
And only one of those involve a shirt.

00:03:29.570 --> 00:03:33.700
So the probability of B given A is 1/3.

00:03:33.700 --> 00:03:34.664
And then finally we can think about

00:03:34.664 --> 00:03:36.473
probability of A and B.

00:03:36.473 --> 00:03:40.395
So the probability, probability,

00:03:40.395 --> 00:03:47.842
of A and B, A and B.

00:03:47.842 --> 00:03:52.620
So this is the probability
of picking a blue shirt.

00:03:52.620 --> 00:03:55.752
So only one out of the six
equally likely outcomes

00:03:55.752 --> 00:03:57.376
is a blue shirt.

00:03:57.376 --> 00:03:58.754
So this one right over here

00:03:58.754 --> 00:04:02.302
is going to be one, one over six.

00:04:02.302 --> 00:04:03.907
So now that we've figured out all of that

00:04:03.907 --> 00:04:05.980
let's see if we can
answer these questions.

00:04:05.980 --> 00:04:08.524
The probability of A given B

00:04:08.524 --> 00:04:10.617
equals the probability of A.

00:04:10.617 --> 00:04:12.900
And that does work out.

00:04:12.900 --> 00:04:13.390
Probability of A given B is 1/2.

00:04:13.390 --> 00:04:15.840
And that's the same thing
as the probability of A.

00:04:15.840 --> 00:04:18.554
The probability that
Tomas likes a blue garment

00:04:18.554 --> 00:04:21.353
given that he has chosen a shirt

00:04:21.353 --> 00:04:23.180
is equal to the probability

00:04:23.180 --> 00:04:24.845
that Tomas likes a blue garment.

00:04:24.845 --> 00:04:25.717
Yep, that's exactly.

00:04:25.717 --> 00:04:27.652
So I guess the words are just rephrasing

00:04:27.652 --> 00:04:30.222
what they wrote here in
a more mathy notation.

00:04:30.222 --> 00:04:32.593
So this is absolutely true.

00:04:32.593 --> 00:04:34.803
The probability of B given A

00:04:34.803 --> 00:04:36.393
is equal to the probability of B.

00:04:36.393 --> 00:04:38.904
Yep, the probability of B given A is 1/3.

00:04:38.904 --> 00:04:40.540
The probability of B is 1/3.

00:04:40.540 --> 00:04:42.696
The probability that Tomas selects a shirt

00:04:42.696 --> 00:04:45.837
given that he has chosen a blue garment

00:04:45.837 --> 00:04:49.130
is equal to the probability
that Tomas selects a shirt.

00:04:49.130 --> 00:04:52.290
Yep, that's right.

00:04:52.290 --> 00:04:56.734
Events A and B are independent events.

00:04:56.734 --> 00:04:58.234
Independent events.

00:04:58.234 --> 00:05:01.608
So two events are independent

00:05:01.608 --> 00:05:05.542
if, well let me write it in math notation.

00:05:05.542 --> 00:05:07.408
These are independent if the probability

00:05:07.408 --> 00:05:11.795
of A given B is equal to

00:05:11.795 --> 00:05:13.749
the probability of A.

00:05:13.749 --> 00:05:15.968
Then we can say A and B are independent.

00:05:15.968 --> 00:05:17.876
Because the probability of A,

00:05:17.876 --> 00:05:19.317
then if this is true then this means

00:05:19.317 --> 00:05:20.652
the probability of A given B

00:05:20.652 --> 00:05:24.100
isn't dependent on
whether B happened or not.

00:05:24.100 --> 00:05:26.564
It's the same thing as
the probability of A.

00:05:26.564 --> 00:05:28.706
This would lead to these
events being indpendent.

00:05:28.706 --> 00:05:31.266
So if you had the probability of B given A

00:05:31.266 --> 00:05:33.451
is equal to the probability of B.

00:05:33.451 --> 00:05:34.370
Same argument.

00:05:34.370 --> 00:05:35.590
That would mean they are independent.

00:05:35.590 --> 00:05:40.344
Or, if we said that the
probability of A and B

00:05:40.344 --> 00:05:44.908
is equal to the probability of A

00:05:44.908 --> 00:05:46.693
times the probability of B

00:05:46.693 --> 00:05:48.775
then this also means they are independent.

00:05:48.775 --> 00:05:49.713
We know that this one is true.

00:05:49.713 --> 00:05:52.217
The probability of A and B is 1/6.

00:05:52.217 --> 00:05:54.933
The probability of A
times the probability of B

00:05:54.933 --> 00:05:57.371
is 1/2 times 1/3 which is 1/6.

00:05:57.371 --> 00:05:59.570
So all of these are clearly true.

00:05:59.570 --> 00:06:02.505
So we can say that A
and B are independent.

00:06:02.505 --> 00:06:04.929
The probability of A is independent

00:06:04.929 --> 00:06:06.625
of whether B has happened or not.

00:06:06.625 --> 00:06:07.817
The probability of B happening

00:06:07.817 --> 00:06:10.465
is independent of whether
A has happened or not.

00:06:10.465 --> 00:06:13.377
The outcome of events A and B

00:06:13.377 --> 00:06:14.922
are dependent on each other.

00:06:14.922 --> 00:06:15.616
No.

00:06:15.616 --> 00:06:17.380
That's the opposite of
saying they are independent.

00:06:17.380 --> 00:06:19.439
So we can cross that out.

00:06:19.439 --> 00:06:21.606
Probably of A and B is equal to

00:06:21.606 --> 00:06:23.483
the probability of A
times the probability of B

00:06:23.483 --> 00:06:25.210
We already said that to be true.

00:06:25.210 --> 00:06:27.418
1/6 is 1/2 times 1/3.

00:06:27.418 --> 00:06:29.284
The probability that Tom selects

00:06:29.284 --> 00:06:30.492
a blue garment that is a shirt

00:06:30.492 --> 00:06:32.675
is equal to the probability that tom

00:06:32.675 --> 00:06:35.227
selects a blue garment
multiplied by the probability

00:06:35.227 --> 00:06:36.478
that he selects a shirt.

00:06:36.478 --> 00:06:37.740
Yep.

00:06:37.740 --> 00:06:39.270
That is absolutely right.

00:06:39.270 --> 00:06:41.720
So actually this is, a lot
of these statements are true.

00:06:41.720 --> 00:06:43.336
The only one that is not

00:06:43.336 --> 00:06:44.529
is that the outcome of events A and B

00:06:44.529 --> 00:06:46.427
are dependent on each other.


Analyzing trends in categorical data

WEBVTT
Kind: captions
Language: en

00:00:00.633 --> 00:00:02.967
Voiceover:The relative
frequency table below

00:00:02.967 --> 00:00:05.663
shows statistics from a
study about the relationship

00:00:05.663 --> 00:00:07.968
between the amount of time a person spends

00:00:07.968 --> 00:00:09.966
using a computer before bed

00:00:09.966 --> 00:00:12.366
and the amount that a
person sleeps each night.

00:00:12.366 --> 00:00:13.567
For computer use,

00:00:13.567 --> 00:00:15.367
each participant was classified

00:00:15.367 --> 00:00:16.839
as minimal, moderate, or extreme.

00:00:16.839 --> 00:00:19.167
Let's look at the frequency table below.

00:00:19.167 --> 00:00:20.033
Let's see.

00:00:20.033 --> 00:00:21.433
That's the frequency table,

00:00:21.433 --> 00:00:21.900
and let's see,

00:00:21.900 --> 00:00:23.834
there's 3 categories of computer time,

00:00:23.834 --> 00:00:24.633
just like they told us,

00:00:24.633 --> 00:00:27.034
minimal, moderate, and extreme.

00:00:27.034 --> 00:00:29.169
This is before they go to bed or at night.

00:00:29.169 --> 00:00:30.700
Then they have the 3 categories

00:00:30.700 --> 00:00:31.833
of how much they're sleeping,

00:00:31.833 --> 00:00:33.433
5 or a few hours per night,

00:00:33.433 --> 00:00:35.033
5 to 7 hours per night,

00:00:35.033 --> 00:00:37.033
or 7 or more hours.

00:00:37.033 --> 00:00:38.566
OK, so that's fair enough.

00:00:38.566 --> 00:00:40.700
Let's see what they want us to do.

00:00:40.700 --> 00:00:44.700
They tell us, "Suppose there
were 17 people in the study

00:00:44.700 --> 00:00:46.833
"who are both in moderate computer users

00:00:46.833 --> 00:00:49.503
"and got 5 to 7 hours of sleep."

00:00:49.503 --> 00:00:51.367
Moderate, 5 to 7.

00:00:51.367 --> 00:00:53.233
This category right over here,

00:00:53.233 --> 00:00:56.633
there are 17 people in
this category over here.

00:00:56.633 --> 00:00:57.967
Just to mark that, let me ...

00:00:57.967 --> 00:01:01.233
I copy and pasted this
chart onto my scratch pad

00:01:01.233 --> 00:01:03.233
so I can write on it.

00:01:03.233 --> 00:01:05.766
This group, they're telling us this group,

00:01:05.766 --> 00:01:07.166
and my pen is really acting up.

00:01:07.166 --> 00:01:09.100
I don't understand what's going on.

00:01:09.100 --> 00:01:12.966
This group right over
here, there are 17 people.

00:01:12.966 --> 00:01:16.766
That group right over there is 17 people.

00:01:16.766 --> 00:01:18.500
Now what are they asking us?

00:01:18.500 --> 00:01:23.500
They're saying, "How
many people in the study

00:01:23.500 --> 00:01:25.900
"were both extreme computer users

00:01:25.900 --> 00:01:28.366
"and got 5 to 7 hours of sleep?

00:01:28.366 --> 00:01:29.700
"Round to the nearest whole number."

00:01:29.700 --> 00:01:32.300
So extreme and got 5 to 7.

00:01:32.300 --> 00:01:33.700
I'll get my scratch pad out.

00:01:33.700 --> 00:01:41.033
They are saying how many
people are in this bucket,

00:01:41.033 --> 00:01:42.555
in this bucket right over here?

00:01:42.663 --> 00:01:44.900
I think I have to replace
my pen tablet or something.

00:01:44.900 --> 00:01:47.888
I don't know why it's getting
all splotchy like this.

00:01:48.350 --> 00:01:49.633
How would we think about this?

00:01:49.633 --> 00:01:51.366
There are 17 people in this group.

00:01:51.366 --> 00:01:53.336
How many people are in this group?

00:01:53.736 --> 00:01:58.434
They tell us that 17 is 34% of the row,

00:01:58.434 --> 00:01:59.833
of the row total,

00:01:59.833 --> 00:02:03.770
so I guess you could say 17 is 34.3%

00:02:03.770 --> 00:02:08.633
of the moderate computer users,

00:02:08.633 --> 00:02:12.397
or you could say that
17 is 30% of the people

00:02:12.397 --> 00:02:15.700
who slept 5 to 7 hours each night,

00:02:15.700 --> 00:02:19.501
or you could say 17 is 10%,

00:02:19.501 --> 00:02:25.500
is 10% of the total number of people.

00:02:25.500 --> 00:02:26.300
Let's just go with that.

00:02:26.300 --> 00:02:28.303
We could figure out the
total number of people.

00:02:28.303 --> 00:02:30.033
So 10%,

00:02:30.371 --> 00:02:31.866
actually, let me write it this way.

00:02:32.701 --> 00:02:37.940
So 10% of the total,

00:02:37.940 --> 00:02:42.701
10% of total is going to be equal to 17,

00:02:42.701 --> 00:02:44.033
or that the total,

00:02:44.033 --> 00:02:45.669
just divide both sides by 10%

00:02:45.669 --> 00:02:48.635
is equal to 17 divided by 10%,

00:02:48.635 --> 00:02:52.766
which is the same thing as 17 over 0.1,

00:02:52.766 --> 00:02:55.633
which, of course, is equal to 170.

00:02:55.633 --> 00:02:57.633
The total is 170,

00:02:57.633 --> 00:02:59.901
and they tell us that extreme,

00:02:59.901 --> 00:03:03.300
extreme computer users represent ...

00:03:03.300 --> 00:03:08.633
extreme computer users who
sleep 5 to 7 hours per night

00:03:08.633 --> 00:03:11.700
represent 11.7%,

00:03:11.700 --> 00:03:14.366
11.7% of the total.

00:03:14.366 --> 00:03:15.766
So the answer to their question

00:03:15.766 --> 00:03:18.167
of how many people were
extreme computer users

00:03:18.167 --> 00:03:20.436
who sleep 5 to 7 hours per night,

00:03:20.436 --> 00:03:24.234
it's 11.7% of 170.

00:03:24.618 --> 00:03:26.151
Let's go back over here.

00:03:26.151 --> 00:03:28.500
We actually have a little
calculator tool here.

00:03:28.500 --> 00:03:33.766
It's 11.7%, which is 0.117,

00:03:33.766 --> 00:03:36.766
times 170,

00:03:36.766 --> 00:03:40.501
times 170 is,

00:03:40.501 --> 00:03:42.834
and let me make sure that
you can see what I'm doing

00:03:42.834 --> 00:03:44.367
by scrolling over a little bit,

00:03:44.367 --> 00:03:48.034
times 170 is equal to 19.89.

00:03:48.034 --> 00:03:49.766
If we're rounding to the nearest whole,

00:03:49.766 --> 00:03:52.166
that's going to be 20 people,

00:03:52.166 --> 00:03:53.800
20 people.

00:03:54.500 --> 00:03:56.966
And then they are going
to ask us some questions.

00:03:56.966 --> 00:03:58.567
They say, "Does the table show evidence

00:03:58.567 --> 00:04:02.233
"of an association between
being a minimal computer user

00:04:02.233 --> 00:04:04.235
"and getting 7 hours of sleep or more?"

00:04:04.235 --> 00:04:05.892
Let's just look at the chart.

00:04:06.366 --> 00:04:09.700
An association between being
a minimal computer user

00:04:09.700 --> 00:04:14.101
and getting 7 hours of sleep or more.

00:04:14.101 --> 00:04:16.966
It looks like minimal computer users,

00:04:17.627 --> 00:04:19.166
these are the minimal computer users

00:04:19.166 --> 00:04:21.833
who get 7 or more hours of sleep.

00:04:21.833 --> 00:04:23.500
There's a couple of ways to read this.

00:04:23.500 --> 00:04:26.835
You could say that 51%
of minimal computer users

00:04:26.835 --> 00:04:28.701
get 7 or more hours of sleep.

00:04:28.701 --> 00:04:31.101
You could say that of the people

00:04:31.101 --> 00:04:33.033
who get 7 or more hours of sleep,

00:04:33.033 --> 00:04:36.033
55% are minimal computer users.

00:04:36.033 --> 00:04:37.166
And of course, this one just says

00:04:37.166 --> 00:04:39.967
that minimal computer users who
get 7 or more hours of sleep

00:04:39.967 --> 00:04:44.393
represent 18.3% of all of
the people who were surveyed.

00:04:44.393 --> 00:04:46.156
Let's look at the choices.

00:04:46.709 --> 00:04:47.967
Actually, before I even
look at the choices,

00:04:47.967 --> 00:04:49.834
let's see if there is an association.

00:04:49.834 --> 00:04:52.500
It does look like if you look at,

00:04:52.500 --> 00:04:54.635
if you look at minimal computer users,

00:04:54.635 --> 00:04:56.839
it looks like a small percentage,

00:04:56.839 --> 00:04:59.367
only 16% get 5 or few hours.

00:04:59.674 --> 00:05:02.166
A higher percentage gets 5 to 7 hours,

00:05:02.166 --> 00:05:04.766
and 51%, the highest percentage,

00:05:04.766 --> 00:05:05.901
gets 7 or more.

00:05:05.901 --> 00:05:09.769
So it looks like for
minimal computer users,

00:05:09.769 --> 00:05:12.981
it looks like the distribution
is definitely weighted

00:05:12.981 --> 00:05:15.901
towards getting more sleep.

00:05:16.193 --> 00:05:18.233
For example, if we look at
the extreme computer users,

00:05:18.233 --> 00:05:19.500
it's the opposite trend.

00:05:20.191 --> 00:05:23.366
It's 47% have 5 or few hours per night,

00:05:23.366 --> 00:05:25.166
33% 5 to 7 hours,

00:05:25.166 --> 00:05:28.100
and then only 19% get 7 or more.

00:05:28.100 --> 00:05:30.966
It looks like the moderate
is someplace in between.

00:05:30.966 --> 00:05:32.233
Just looking at this,

00:05:32.233 --> 00:05:34.366
just looking at each of these rows,

00:05:34.366 --> 00:05:35.566
it looks like there is a trend

00:05:35.566 --> 00:05:38.966
where if you use a computer for less time,

00:05:38.966 --> 00:05:40.900
you are more likely to have more sleep,

00:05:40.900 --> 00:05:42.769
and likewise, if you use a computer more,

00:05:42.769 --> 00:05:44.833
you're more likely to have less sleep.

00:05:44.833 --> 00:05:45.901
Another way to think about it,

00:05:45.901 --> 00:05:46.762
when you look at the people

00:05:46.762 --> 00:05:49.233
who are getting 7 or more hours of sleep,

00:05:49.709 --> 00:05:51.300
a majority of them,

00:05:51.300 --> 00:05:54.633
a majority of them are
minimal computer users,

00:05:54.633 --> 00:05:55.767
and there's 3 categories.

00:05:55.767 --> 00:05:58.041
So for 55% to be minimal computer users

00:05:58.041 --> 00:06:00.448
really does feel like the
minimal computer users

00:06:00.448 --> 00:06:01.833
are more ...

00:06:03.002 --> 00:06:05.566
they're definitely more
disproportionately representing

00:06:05.566 --> 00:06:07.301
the people who are getting 7 ...

00:06:07.301 --> 00:06:09.769
or disproportionally
represented in this category

00:06:09.769 --> 00:06:12.500
of 7 or more hours of sleep.

00:06:12.500 --> 00:06:15.434
You see that the extreme
computer users in this category,

00:06:15.434 --> 00:06:18.301
they represent only 20% of this category.

00:06:18.301 --> 00:06:20.433
So it does look like
there is an association

00:06:20.433 --> 00:06:22.033
between minimal computer use

00:06:22.033 --> 00:06:24.100
and getting 7 or more hours of sleep.

00:06:24.100 --> 00:06:27.066
But let's look at the
actual choices they give us.

00:06:27.303 --> 00:06:28.966
Does the table show
evidence of association

00:06:28.966 --> 00:06:30.501
between a minimal computer user

00:06:30.501 --> 00:06:32.835
and getting 7 hours of sleep or more?

00:06:32.900 --> 00:06:37.166
Yes, because 35.1% are
extreme computer users,

00:06:37.166 --> 00:06:39.393
and 29.1% of people are moderate.

00:06:40.100 --> 00:06:41.700
I go with the yes, but this doesn't seem

00:06:41.700 --> 00:06:43.534
to really back up the claim.

00:06:43.965 --> 00:06:45.900
This is just giving us some random data

00:06:45.900 --> 00:06:47.833
about the percentage that
are extreme computer users

00:06:47.833 --> 00:06:49.600
or moderate computer users.

00:06:50.033 --> 00:06:50.633
No ...

00:06:50.633 --> 00:06:51.500
well ...

00:06:52.623 --> 00:06:54.700
I explained why I go with yes,

00:06:54.700 --> 00:06:55.965
that there does seem to be a trend,

00:06:55.965 --> 00:06:57.366
and I don't even believe
what this statement is

00:06:57.366 --> 00:06:58.700
because the total column percentages

00:06:58.700 --> 00:07:00.035
are essentially equal.

00:07:00.035 --> 00:07:01.372
We see that the total column ...

00:07:01.680 --> 00:07:03.767
that the column percentages,

00:07:03.767 --> 00:07:06.166
the column percentages are not equal

00:07:06.166 --> 00:07:07.767
for the various,

00:07:07.767 --> 00:07:12.133
for people who are getting
7 hours or more of sleep.

00:07:12.166 --> 00:07:13.166
We see that right over here,

00:07:13.166 --> 00:07:15.833
55, 25, 20,

00:07:15.833 --> 00:07:18.101
so I won't go with that one either.

00:07:18.101 --> 00:07:22.118
Yes, because 51% of minimal computer users

00:07:22.118 --> 00:07:23.566
get 7 or more hours of sleep,

00:07:23.566 --> 00:07:25.927
and only 33% of all computer users

00:07:26.357 --> 00:07:28.701
get 7 or more hours.

00:07:28.701 --> 00:07:29.167
Yeah.

00:07:29.167 --> 00:07:30.966
I mean that seems pretty good.

00:07:30.966 --> 00:07:33.433
51% of minimal computer users

00:07:33.433 --> 00:07:34.966
get 7 or more hours of sleep,

00:07:34.966 --> 00:07:38.575
and only 33% of all computer users

00:07:38.575 --> 00:07:41.633
get 7 or more hours of sleep.

00:07:41.633 --> 00:07:43.500
That looks like a pretty good explanation,

00:07:43.500 --> 00:07:44.566
so I'll check that,

00:07:44.566 --> 00:07:46.068
but let's just review all of them.

00:07:46.966 --> 00:07:47.366
No.

00:07:47.366 --> 00:07:49.033
Well, I already said I think it's yes,

00:07:49.033 --> 00:07:50.833
but because the total
percentage of extreme users

00:07:50.833 --> 00:07:52.300
who get 5 to 7 hours of sleep

00:07:52.300 --> 00:07:54.300
is the same as the total percentage

00:07:54.300 --> 00:07:55.567
of moderate computer users

00:07:55.567 --> 00:07:58.733
who get 5 to 7 hours of sleep.

00:07:58.966 --> 00:08:00.719
So that doesn't really meet,

00:08:00.719 --> 00:08:03.366
it's not touching on the
point that we're looking for.

00:08:03.366 --> 00:08:06.484
Yes, because 55% of people who get 75 ...

00:08:06.823 --> 00:08:10.366
who get 7 or more hours
are minimal computer users,

00:08:10.366 --> 00:08:13.976
and only 35% of all people
are minimal computer users.

00:08:13.976 --> 00:08:15.002
Actually, I'll go with this as well.

00:08:15.002 --> 00:08:16.905
Oh yeah, this is a multi-select here,

00:08:16.905 --> 00:08:18.636
so I could select that one as well.

00:08:18.636 --> 00:08:20.636
This one, we're looking at of the ...

00:08:20.636 --> 00:08:23.433
so here, we looked at the percentage

00:08:23.433 --> 00:08:24.566
of minimal computer users

00:08:24.566 --> 00:08:26.433
who get 7 hours of sleep,

00:08:26.433 --> 00:08:28.101
and we saw that percentage is higher

00:08:28.101 --> 00:08:29.906
than for the whole population.

00:08:29.906 --> 00:08:32.366
Here, we're looking at the people

00:08:32.366 --> 00:08:34.366
who get 7 or more hours of sleep,

00:08:34.366 --> 00:08:36.833
and we're saying 55% of them,

00:08:36.833 --> 00:08:42.366
55% of them are minimal computer users

00:08:42.366 --> 00:08:45.434
even though only 35% of all the people

00:08:45.434 --> 00:08:46.701
are minimal computer users.

00:08:46.701 --> 00:08:48.367
So I would go with both of these.

00:08:48.367 --> 00:08:51.366
And so let us check our answer,

00:08:51.366 --> 00:08:52.935
and we got it right.


Filling out frequency table for independent events

WEBVTT
Kind: captions
Language: en

00:00:00.838 --> 00:00:02.973
Voiceover:One rainy Saturday morning,

00:00:02.973 --> 00:00:06.165
Adam woke up to hear his mom complaining

00:00:06.165 --> 00:00:07.811
about the house being dirty.

00:00:07.811 --> 00:00:10.789
"Mom is always grouchy when it rains,"

00:00:10.789 --> 00:00:12.949
Adam's brother said to him.

00:00:12.949 --> 00:00:14.982
So Adam decided to figure out

00:00:14.982 --> 00:00:17.214
if this statement was actually true.

00:00:17.214 --> 00:00:18.261
For the next year,

00:00:18.261 --> 00:00:20.163
he charted every time it rained

00:00:20.163 --> 00:00:22.316
and every time his mom was grouchy.

00:00:22.316 --> 00:00:24.164
What he found was very interesting.

00:00:24.164 --> 00:00:26.483
Rainy days and his mom being grouchy

00:00:26.483 --> 00:00:29.611
were entirely independent events.

00:00:29.611 --> 00:00:32.154
Some of his data are
shown in the table below.

00:00:32.154 --> 00:00:35.139
Fill in the missing values
from the frequency table.

00:00:36.046 --> 00:00:39.945
Let's see, we have raining
days and not raining days

00:00:39.945 --> 00:00:42.330
and the total days that
he kept the data for.

00:00:42.330 --> 00:00:43.751
And then he tabulated on or let's say,

00:00:43.751 --> 00:00:45.168
the raining days whether his mom

00:00:45.168 --> 00:00:46.720
was grouchy or not grouchy.

00:00:46.720 --> 00:00:48.447
And on a not raining day whether his mom

00:00:48.447 --> 00:00:51.191
was grouchy or not grouchy.

00:00:51.191 --> 00:00:53.248
And there's a total of 35 days it rained,

00:00:53.248 --> 00:00:56.119
330 days that it didn't rain.

00:00:56.119 --> 00:01:02.052
And then 73 times his mom was grouchy

00:01:02.052 --> 00:01:06.400
and 292 times his mom was not grouchy.

00:01:06.400 --> 00:01:08.625
So the first thing is how
do we figure this out?

00:01:08.625 --> 00:01:10.256
We have these 4 boxes here.

00:01:10.256 --> 00:01:12.383
It's not clear that we can just...

00:01:12.383 --> 00:01:15.120
we have enough information to fill it out

00:01:15.120 --> 00:01:16.448
just with this table.

00:01:16.448 --> 00:01:18.232
But we have to remember what they told us.

00:01:18.232 --> 00:01:21.283
They told us that his mom being grouchy

00:01:21.283 --> 00:01:26.113
and it raining were
entirely independent events.

00:01:26.113 --> 00:01:29.937
Another way of saying that
is the probability of his...

00:01:29.937 --> 00:01:31.999
Let me do this in color that
you're more likely to see.

00:01:31.999 --> 00:01:33.239
Another way of saying that...

00:01:33.239 --> 00:01:34.304
So independent events,

00:01:34.304 --> 00:01:36.295
that means that the probability...

00:01:36.295 --> 00:01:38.230
My pen is acting up a little bit.

00:01:38.230 --> 00:01:40.119
Probability that mom is grouchy.

00:01:40.119 --> 00:01:40.832
So let me write that.

00:01:40.832 --> 00:01:41.743
Mom...

00:01:41.743 --> 00:01:42.544
My pen is really...

00:01:42.544 --> 00:01:54.347
Mom is grouchy given it is raining.

00:01:54.347 --> 00:01:56.715
It shouldn't really matter
whether it's raining.

00:01:56.715 --> 00:01:59.106
It should just be the same
thing as the probability

00:01:59.106 --> 00:02:08.100
of mom being grouchy in general.

00:02:08.100 --> 00:02:09.195
So what does that tell us?

00:02:09.195 --> 00:02:11.131
Well we can figure out the probability

00:02:11.131 --> 00:02:13.443
that mom is grouchy in general.

00:02:13.443 --> 00:02:17.507
She's grouchy 73 out of 365 days.

00:02:17.507 --> 00:02:21.173
So the probability that
mom is grouchy in general

00:02:21.173 --> 00:02:31.355
is going to be 73 divided by 365.

00:02:31.913 --> 00:02:33.492
And so [are these] just
based on the data we have.

00:02:33.492 --> 00:02:36.145
That's the best estimate
that mom is grouchy.

00:02:36.145 --> 00:02:37.923
The probability that mom is grouchy.

00:02:37.923 --> 00:02:40.705
It's the percentage of days
that she's been grouchy.

00:02:40.705 --> 00:02:42.888
So that is .2.

00:02:42.888 --> 00:02:45.664
So based on the data,

00:02:45.664 --> 00:02:47.025
the best estimate of the probability

00:02:47.025 --> 00:02:52.824
of mom being grouchy is .2 or 20%.

00:02:52.824 --> 00:02:54.680
And so we should have the probability

00:02:54.680 --> 00:02:56.912
of mom being grouchy
given that it's raining

00:02:56.912 --> 00:02:58.849
should be 20% as well.

00:02:58.849 --> 00:02:59.761
So this number...

00:02:59.761 --> 00:03:01.024
So given that it's raining,

00:03:01.024 --> 00:03:03.080
we should also have 20% of the time,

00:03:03.080 --> 00:03:04.250
mom is grouchy because

00:03:04.250 --> 00:03:05.297
these are independent events.

00:03:05.297 --> 00:03:06.649
It shouldn't matter whether
it's raining or not.

00:03:06.649 --> 00:03:07.970
This should be 20%...

00:03:10.507 --> 00:03:13.667
She should be grouchy 20%
of time that it's raining

00:03:13.667 --> 00:03:15.508
and she should be grouchy 20% of the time

00:03:15.508 --> 00:03:16.779
that it's not raining.

00:03:16.779 --> 00:03:18.960
That's what would be
consistent with the data

00:03:18.960 --> 00:03:22.735
saying that these were
entirely independent events.

00:03:22.735 --> 00:03:25.057
So what is 20% of 35?

00:03:25.057 --> 00:03:26.919
Well 20% is 1/5th.

00:03:26.919 --> 00:03:30.260
1/5th of 35 is 7.

00:03:30.260 --> 00:03:31.255
And once again,

00:03:31.255 --> 00:03:33.919
all I did is I said 20% of 35 is 7.

00:03:33.919 --> 00:03:38.591
And if that's 7 then 35 minus 7.

00:03:38.591 --> 00:03:41.735
That's gonna be 28 right over there.

00:03:41.735 --> 00:03:44.111
And then if this is 7,

00:03:44.111 --> 00:03:51.535
then 73 minus 7 is going to be 66.

00:03:51.535 --> 00:03:54.518
And 330...

00:03:54.518 --> 00:03:56.095
I guess there's a couple
of way we could do it.

00:03:56.095 --> 00:03:56.870
We could take...

00:03:56.870 --> 00:04:02.270
Actually we could just take 292 minus 28

00:04:02.270 --> 00:04:03.663
is going to be...

00:04:03.663 --> 00:04:07.727
Let's see 292 minus 8 would be 284.

00:04:07.727 --> 00:04:11.192
Minus another 20, 264.

00:04:11.445 --> 00:04:12.285
And do the numbers all add up?

00:04:12.285 --> 00:04:12.828
Yes.

00:04:12.828 --> 00:04:17.349
66 plus 264 is 330.

00:04:17.349 --> 00:04:19.133
So the key realization here is

00:04:19.133 --> 00:04:21.254
what he's saying he found
was very interesting.

00:04:21.254 --> 00:04:22.941
Rainy days and his mom being grouchy

00:04:22.941 --> 00:04:25.324
were entirely independent events.

00:04:25.324 --> 00:04:26.652
That means that the probability

00:04:26.652 --> 00:04:28.580
of his mom being grouchy...

00:04:28.580 --> 00:04:30.389
It shouldn't matter whether
it's raining or not.

00:04:30.389 --> 00:04:31.420
It should just be...

00:04:31.420 --> 00:04:33.116
It should be the same probability

00:04:33.116 --> 00:04:34.557
of whether it's raining or not.

00:04:34.557 --> 00:04:36.316
And our best estimate of the probability

00:04:36.316 --> 00:04:38.077
of his mom being grouchy is

00:04:38.077 --> 00:04:40.212
on the total days, is 20%.

00:04:40.212 --> 00:04:41.661
And so if the data's backing up

00:04:41.661 --> 00:04:43.157
that it's independent events

00:04:43.157 --> 00:04:45.229
then the best way to
fill this out would be

00:04:45.229 --> 00:04:48.509
the probability of his mom being grouchy

00:04:48.509 --> 00:04:52.004
on a rainy day or not rainy
day should be the same.

00:04:52.004 --> 00:04:55.148
And that's what we filled
out right over here.


Comparing means of distributions

WEBVTT
Kind: captions
Language: en

00:00:00.700 --> 00:00:02.433
Voiceover:Kenny interviewed
freshmen and seniors

00:00:02.433 --> 00:00:03.301
at his high school,

00:00:03.301 --> 00:00:07.700
asking them how many pieces
of fruit they eat each day.

00:00:07.700 --> 00:00:10.968
The results are shown
in the 2 plots below.

00:00:10.968 --> 00:00:13.366
The first statement
that we have to complete

00:00:13.366 --> 00:00:16.036
is the mean number of
fruits is greater for,

00:00:16.036 --> 00:00:18.312
and actually, let me go
down the actual screen,

00:00:18.312 --> 00:00:19.366
is greater for,

00:00:19.366 --> 00:00:22.435
we have to pick between
freshmen and seniors.

00:00:22.435 --> 00:00:24.174
Then they said the mean is a good measure

00:00:24.174 --> 00:00:26.366
for the center of distribution of,

00:00:26.366 --> 00:00:28.500
and we pick either freshmen or seniors.

00:00:28.500 --> 00:00:30.646
Let me go back to my scratch pad here,

00:00:30.646 --> 00:00:32.786
and let's think about this.

00:00:32.971 --> 00:00:34.500
Let's first think about the first part.

00:00:34.500 --> 00:00:36.767
Let's just calculate the mean

00:00:36.767 --> 00:00:38.633
for each of these distributions.

00:00:38.633 --> 00:00:42.033
I encourage you to pause the video

00:00:42.033 --> 00:00:44.700
and try to calculate it out on your own.

00:00:44.700 --> 00:00:46.233
Let's first think about
the mean number of fruit

00:00:46.233 --> 00:00:47.100
for freshmen.

00:00:47.100 --> 00:00:48.167
Essentially, we're just going to take

00:00:48.167 --> 00:00:49.700
each of these data points,

00:00:49.700 --> 00:00:51.233
add them all together,

00:00:51.233 --> 00:00:52.974
and then divide by the
number of data points

00:00:52.974 --> 00:00:54.100
that we have.

00:00:54.100 --> 00:00:56.902
We have one data point at 0.

00:00:56.902 --> 00:00:58.700
We have one data point at 0,

00:00:58.700 --> 00:01:00.233
so I'll write 0.

00:01:00.233 --> 00:01:04.233
And then we have two data points at 1,

00:01:04.233 --> 00:01:07.833
so we could say plus 2 times 1.

00:01:07.833 --> 00:01:11.033
And then we have two data points at 2,

00:01:11.033 --> 00:01:14.771
so you write plus 2 times 2.

00:01:14.771 --> 00:01:17.368
And then, let's see, we
have a bunch of data.

00:01:17.368 --> 00:01:19.768
We have four data points at 3,

00:01:19.768 --> 00:01:21.700
so we could say we have four 3s.

00:01:21.700 --> 00:01:23.100
Let me circle that.

00:01:23.100 --> 00:01:26.300
So we have four 3s,

00:01:26.300 --> 00:01:29.033
plus 4 times 3.

00:01:29.033 --> 00:01:33.700
And then we have three 4s,

00:01:33.700 --> 00:01:37.300
so plus 3 times 4.

00:01:37.300 --> 00:01:40.167
And then we have a 5,

00:01:40.167 --> 00:01:42.100
so plus 5,

00:01:42.100 --> 00:01:44.033
and then we have a 6.

00:01:44.033 --> 00:01:45.700
Let me do this in a
color that you can see.

00:01:45.700 --> 00:01:47.774
And then we have a 6 right over here,

00:01:47.774 --> 00:01:48.967
plus 6.

00:01:48.967 --> 00:01:50.833
How many total points did we have?

00:01:50.833 --> 00:01:59.523
We had 1, 2, 3, 4, 5, 6, 7,
8, 9, 10, 11, 12, 13, 14,

00:01:59.523 --> 00:02:00.490
oh, actually, be careful.

00:02:00.490 --> 00:02:02.766
We had 15 points and I
didn't put that one in there.

00:02:02.766 --> 00:02:04.568
Actually, let me just ...

00:02:04.568 --> 00:02:06.566
So we have 15 points,

00:02:06.566 --> 00:02:08.566
and I can't forget this one over here,

00:02:08.566 --> 00:02:09.900
so plus ...

00:02:09.900 --> 00:02:11.700
my pen is acting a little funny right now,

00:02:11.700 --> 00:02:13.168
but we'll power through that,

00:02:13.168 --> 00:02:17.248
plus 19.

00:02:17.248 --> 00:02:18.900
So what is this going to be?

00:02:18.900 --> 00:02:20.900
This is just going to be 0.

00:02:20.900 --> 00:02:22.566
This is going to be 2.

00:02:22.566 --> 00:02:24.166
This is going to be 4.

00:02:24.166 --> 00:02:25.901
This is going to be 12.

00:02:25.901 --> 00:02:27.101
My pen is really acting up.

00:02:27.101 --> 00:02:28.700
It's almost like it's
running out of digital ink

00:02:28.700 --> 00:02:30.033
or something.

00:02:30.033 --> 00:02:32.301
This is going to be another 12,

00:02:32.301 --> 00:02:34.033
and then we have 5, 6, and 19.

00:02:34.033 --> 00:02:34.833
So what is this going to be?

00:02:34.833 --> 00:02:38.101
2 plus 4 is 6,

00:02:38.101 --> 00:02:40.304
plus 24 is 30,

00:02:40.304 --> 00:02:44.233
plus 11 is 41,

00:02:44.233 --> 00:02:48.233
plus 19 gets us to 60.

00:02:48.233 --> 00:02:51.166
60 divided by 15 is 4,

00:02:51.166 --> 00:02:53.531
so the mean number of fruit per day

00:02:53.531 --> 00:02:57.034
for the freshmen is 4
pieces of fruit per day.

00:02:57.034 --> 00:02:58.434
This right over here,

00:02:58.434 --> 00:03:01.500
that right over there
is our mean for the ...

00:03:01.500 --> 00:03:04.366
Let me put that in a color
that you can actually see.

00:03:04.366 --> 00:03:07.366
Now let's do the same
calculation for the seniors.

00:03:07.704 --> 00:03:10.100
We have one data point where they didn't

00:03:10.100 --> 00:03:13.515
eat any fruit at all each
day, not too healthy.

00:03:13.515 --> 00:03:15.038
Then you have one 1,

00:03:15.038 --> 00:03:16.300
so I'll just write that as,

00:03:16.300 --> 00:03:18.034
we could actually write that as 1 times 1,

00:03:18.034 --> 00:03:19.633
but I'll just write that as 1.

00:03:19.633 --> 00:03:21.700
Then we have two 2s,

00:03:21.700 --> 00:03:25.100
so plus 2 times 2.

00:03:25.100 --> 00:03:29.768
Then we have one, two
, three, four, five 3s,

00:03:29.768 --> 00:03:32.166
five 3s,

00:03:32.166 --> 00:03:35.433
so plus 5 times 3.

00:03:35.433 --> 00:03:41.233
And then we have three 4s,

00:03:41.233 --> 00:03:44.233
so plus 3 times 4.

00:03:44.233 --> 00:03:48.900
And then we have two 5s,

00:03:48.900 --> 00:03:51.433
plus 2 times 5,

00:03:51.433 --> 00:03:53.767
and then we have a 6.

00:03:53.767 --> 00:03:55.167
We have a 6,

00:03:55.167 --> 00:03:56.634
plus 6,

00:03:56.634 --> 00:03:58.100
and we have a 7,

00:03:58.100 --> 00:04:01.233
someone eats 7 pieces of fruit each day,

00:04:01.233 --> 00:04:02.433
a lot of fiber,

00:04:02.433 --> 00:04:03.967
plus 7.

00:04:03.967 --> 00:04:06.766
And now, how many data points did we have?

00:04:06.766 --> 00:04:14.433
We have 1, 2, 3, 4, 5, 6, 7,
8, 9, 10, 11, 12, 13, 14, 15,

00:04:14.433 --> 00:04:16.366
16 data points.

00:04:16.366 --> 00:04:20.235
So we're going to divide this by 16.

00:04:20.235 --> 00:04:21.566
So what is this going to be?

00:04:21.566 --> 00:04:22.900
This is just 0.

00:04:22.900 --> 00:04:23.500
Let's see.

00:04:23.500 --> 00:04:25.712
This is, just right over, that's 0.

00:04:25.712 --> 00:04:27.847
This is 4.

00:04:27.847 --> 00:04:30.100
This is 15.

00:04:30.100 --> 00:04:32.572
This is 12.

00:04:32.572 --> 00:04:34.567
This is 10.

00:04:34.567 --> 00:04:38.233
So we have 1 plus 4 is 5 plus 15 is 20

00:04:38.233 --> 00:04:40.100
plus 12 is 32

00:04:40.100 --> 00:04:43.384
plus 10 is 42.

00:04:43.384 --> 00:04:47.100
42 plus 6 is 48,

00:04:47.100 --> 00:04:48.848
48.

00:04:48.848 --> 00:04:50.034
Am I doing ...

00:04:50.034 --> 00:04:54.839
42 plus 6 is 48 plus 7,

00:04:54.839 --> 00:04:57.366
48 plus 7 is 55.

00:04:57.366 --> 00:04:58.034
Did I do that right?

00:04:58.034 --> 00:04:58.900
Let me do that one more time.

00:04:58.900 --> 00:05:00.307
1 plus 4 is 5

00:05:00.307 --> 00:05:01.966
plus 15 is 20,

00:05:01.966 --> 00:05:04.634
32, 42.

00:05:04.634 --> 00:05:07.034
42 plus 13 is 55.

00:05:07.034 --> 00:05:13.166
So this is equal to 55 over 16,

00:05:13.166 --> 00:05:15.100
which is the same thing as, let's see,

00:05:15.100 --> 00:05:19.900
that's the same thing as 3 and 3 that ...

00:05:19.900 --> 00:05:22.566
3 times 16 is 48,

00:05:22.566 --> 00:05:26.300
so 3 and 7/16.

00:05:26.300 --> 00:05:33.434
So the mean for the seniors, 3 and 7/16,

00:05:33.434 --> 00:05:34.700
that's right around ...

00:05:34.700 --> 00:05:34.966
let's see.

00:05:34.966 --> 00:05:36.900
This is 3, that's 4, so 7/16,

00:05:36.900 --> 00:05:39.512
it's a little less than a half.

00:05:39.512 --> 00:05:42.834
It's right around there.

00:05:42.834 --> 00:05:45.966
So the mean number of
fruits is defnitely greater

00:05:45.966 --> 00:05:47.100
for the freshmen.

00:05:47.100 --> 00:05:48.689
They have 4 ...

00:05:48.689 --> 00:05:51.368
Their mean number of
fruit eaten per day is 4

00:05:51.368 --> 00:05:53.633
versus 3 and 7/16.

00:05:53.633 --> 00:05:54.633
The mean is a good measure

00:05:54.633 --> 00:05:57.100
for the center of the distribution of.

00:05:57.100 --> 00:06:00.792
So when we think about whether
it's freshmen or seniors,

00:06:00.792 --> 00:06:05.633
the mean is fairly sensitive
to when you have outliers here.

00:06:05.633 --> 00:06:07.233
For example, someone here was eating

00:06:07.233 --> 00:06:10.633
19 pieces of fruit per day.

00:06:10.633 --> 00:06:12.433
That's an enormous amount of fruit.

00:06:12.433 --> 00:06:13.767
They must be only eating fruit.

00:06:13.767 --> 00:06:15.914
You can imagine if it
was even a bigger number,

00:06:15.914 --> 00:06:18.100
if someone was eating 20
or 30 pieces of fruit,

00:06:18.100 --> 00:06:22.433
just that one data point will
skew the entire mean upwards.

00:06:22.433 --> 00:06:24.233
That wouldn't be the effect on the mode

00:06:24.233 --> 00:06:25.900
because the mode is a middle number.

00:06:25.900 --> 00:06:27.173
Even if you change this one point

00:06:27.173 --> 00:06:28.507
all the way out here,

00:06:28.507 --> 00:06:31.300
it's not going to change
what the middle number is.

00:06:31.300 --> 00:06:34.766
So the mean is more
sensitive to these outliers,

00:06:34.766 --> 00:06:35.966
to these really,

00:06:35.966 --> 00:06:37.700
these points that are really, really high,

00:06:37.700 --> 00:06:38.834
really, really low.

00:06:38.834 --> 00:06:42.302
And because the seniors don't seem to have

00:06:42.302 --> 00:06:43.900
any outliers like that,

00:06:43.900 --> 00:06:45.700
I would say that the
mean is a good measure

00:06:45.700 --> 00:06:48.634
for the center of
distribution for the seniors,

00:06:48.634 --> 00:06:50.989
or a better measure for
the center of distribution

00:06:50.989 --> 00:06:52.286
for the seniors.

00:06:52.286 --> 00:06:54.289
Let's fill both of those out.

00:06:54.658 --> 00:06:58.369
The mean number of fruit is
greater for the freshmen,

00:06:58.369 --> 00:07:00.435
and the mean is a good measure

00:07:00.435 --> 00:07:05.366
for the center of
distribution for the seniors.

00:07:05.366 --> 00:07:06.439
You actually even see it here.

00:07:06.439 --> 00:07:09.302
We saw that the mean number
for freshmen was at 4,

00:07:09.302 --> 00:07:12.100
but if you just ignored
this person right over here

00:07:12.100 --> 00:07:13.233
and just you thought about the bulk

00:07:13.233 --> 00:07:15.100
of this distribution right over here,

00:07:15.100 --> 00:07:17.184
4 really doesn't look
like the center of it.

00:07:17.184 --> 00:07:19.966
The center of it looks closer to 3 here.

00:07:19.966 --> 00:07:21.567
What happened is this one person

00:07:21.567 --> 00:07:23.766
eating 19 pieces of fruit per day

00:07:23.766 --> 00:07:25.500
skewed the mean upwards.

00:07:25.500 --> 00:07:29.033
While here, that 3 and
7/16 really did look closer

00:07:29.033 --> 00:07:30.967
to the actual distribution,

00:07:30.967 --> 00:07:31.900
closer to the ...

00:07:31.900 --> 00:07:32.960
actually, I shouldn't say ...

00:07:32.960 --> 00:07:33.968
I mean in both times,

00:07:33.968 --> 00:07:35.300
we actually did calculate the mean

00:07:35.300 --> 00:07:37.033
of the actual distribution.

00:07:37.033 --> 00:07:38.900
But here, since there's no outliers,

00:07:38.900 --> 00:07:41.700
it does seem the mean
seemed much closer to,

00:07:41.700 --> 00:07:44.702
I guess you could say
the middle of this pile

00:07:44.702 --> 00:07:45.967
right over here.

00:07:45.967 --> 00:07:47.180
Let's check our answer,

00:07:47.180 --> 00:07:48.800
and we got it right.


Means and medians of different distributions

WEBVTT
Kind: captions
Language: en

00:00:00.467 --> 00:00:02.955
Voiceover:"For a senior
project, Richard is researching

00:00:02.955 --> 00:00:04.923
"how much money a college graduate can

00:00:04.923 --> 00:00:07.699
"expect to earn based on his or her major.

00:00:07.699 --> 00:00:10.443
"He finds the following interesting facts:

00:00:10.443 --> 00:00:13.393
"Basketball superstar Michael Jordan was a

00:00:13.393 --> 00:00:16.925
"geology major at the
University of North Carolina.

00:00:16.925 --> 00:00:19.203
"There were only three
civil engineering majors

00:00:19.203 --> 00:00:20.839
"from the University of Montana.

00:00:20.839 --> 00:00:22.765
"They all took the exact same job

00:00:22.765 --> 00:00:25.795
at the same company,
earning the same salary.

00:00:25.795 --> 00:00:29.771
"Of the 35 finance majors
from Wesleyan University,

00:00:29.771 --> 00:00:32.756
"32 got high-paying consulting jobs,

00:00:32.756 --> 00:00:35.185
"and the other 3 were unemployed.

00:00:35.185 --> 00:00:37.411
"For geology majors from the University of

00:00:37.411 --> 00:00:40.699
"North Carolina the median
income will likely be ..."

00:00:40.699 --> 00:00:42.131
and we have some options here,

00:00:42.131 --> 00:00:44.972
"less than, equal to or
greater than the mean."

00:00:44.972 --> 00:00:46.681
And then we have to answer
the same questions ...

00:00:46.681 --> 00:00:48.907
"For civil engineering
majors from Montana,

00:00:48.907 --> 00:00:50.114
the median income ..."

00:00:50.114 --> 00:00:51.979
Well actually these are both about median.

00:00:51.979 --> 00:00:53.260
"The median income will be ..."

00:00:53.260 --> 00:00:54.902
and we compare it against the mean.

00:00:54.902 --> 00:00:56.988
And then, "For finance
majors from Wesleyan ..."

00:00:56.988 --> 00:00:59.409
We're going to compare the
median income to the mean.

00:00:59.409 --> 00:01:01.163
So to visualize this a little bit more,

00:01:01.163 --> 00:01:03.130
I've copied and pasted
this exact same problem

00:01:03.130 --> 00:01:07.795
onto my scratchpad, so here it
is, I can now write on this.

00:01:07.795 --> 00:01:10.447
So, let's think about each of these.

00:01:10.447 --> 00:01:13.959
"For geology majors from UNC,

00:01:13.959 --> 00:01:16.076
"the median income will likely be ..."

00:01:16.076 --> 00:01:18.070
How will that compare to the mean?

00:01:18.070 --> 00:01:19.683
Well what do they tell us about UNC?

00:01:19.683 --> 00:01:23.251
They tell us that Michael
Jordan was a geology major

00:01:23.251 --> 00:01:25.190
at the University of North Carolina.

00:01:25.190 --> 00:01:26.987
So what will the distribution

00:01:26.987 --> 00:01:28.814
of salaries probably look like?

00:01:28.814 --> 00:01:30.583
So if we're thinking
about the University of

00:01:30.583 --> 00:01:33.510
North Carolina, probably will
look something like this.

00:01:33.510 --> 00:01:37.869
And I'm going to do a
very rough distribution

00:01:37.869 --> 00:01:39.785
right over here and let's
say that this would be

00:01:39.785 --> 00:01:44.968
a salary of 0, and let's say
that is a salary of, I don't know

00:01:44.968 --> 00:01:49.480
Let me put a salary of 50K
here, I'll do this in thousands.

00:01:49.480 --> 00:01:52.920
Let's say this is 100
thousand right over here.

00:01:52.920 --> 00:01:55.348
And then you have Michael Jordan who is,

00:01:55.348 --> 00:01:58.344
actually I'll do a little gap
here because he's so far up,

00:01:58.344 --> 00:02:00.143
I don't know exactly what he was making

00:02:00.143 --> 00:02:02.985
but it was definitely
in the tens of millions

00:02:02.985 --> 00:02:06.092
of dollars a year so Michael Jordan is

00:02:06.092 --> 00:02:09.577
way, way, way, way, up here.

00:02:09.700 --> 00:02:12.883
So if you were to make a histogram or a

00:02:12.883 --> 00:02:14.788
plot of all of the salaries we could say,

00:02:14.788 --> 00:02:16.931
Okay well you know maybe
we have, if you put all

00:02:16.931 --> 00:02:19.729
of the folks from geology majors at

00:02:19.729 --> 00:02:20.796
University of North Carolina...

00:02:20.796 --> 00:02:23.320
well there's probably, especially
right when they graduated

00:02:23.320 --> 00:02:27.112
there's probably you know, 1,
2, 3, I could keep doing it.

00:02:27.112 --> 00:02:29.112
A bunch of people maybe making 50K maybe

00:02:29.112 --> 00:02:31.392
some people making a
little bit more, maybe some

00:02:31.392 --> 00:02:35.030
people up here, maybe some people there.

00:02:35.030 --> 00:02:37.741
Some people there, some people there.

00:02:37.741 --> 00:02:40.376
Right there, maybe someone's making 100K.

00:02:40.376 --> 00:02:43.480
Maybe it's a couple of people up there,

00:02:43.480 --> 00:02:45.776
maybe someone isn't making anything,

00:02:45.776 --> 00:02:47.824
maybe they weren't able to find a job.

00:02:47.824 --> 00:02:49.296
And then of course you have Michael Jordan

00:02:49.296 --> 00:02:51.560
up here making you
know, 10 million dollars

00:02:51.560 --> 00:02:53.861
or 20 million dollars
or something like that.

00:02:53.861 --> 00:02:55.584
So when you have a situation like this

00:02:55.584 --> 00:02:58.622
where you have this
outlier of Michael Jordan

00:02:58.622 --> 00:03:01.404
it's going to put, one
way I think about it

00:03:01.404 --> 00:03:03.813
it kind of tugs on the
mean, it wouldn't affect

00:03:03.813 --> 00:03:05.448
the median because remember the median is

00:03:05.448 --> 00:03:08.400
the middle value so it
doesn't matter how high

00:03:08.400 --> 00:03:11.307
this number is, you can
make this a trillion dollars

00:03:11.307 --> 00:03:13.601
it's not going to change
what the middle value is.

00:03:13.601 --> 00:03:15.904
The middle value is still
going to be the same

00:03:15.904 --> 00:03:18.344
middle value, you can
move this anywhere around

00:03:18.344 --> 00:03:20.877
in this range it's not
going to change the median.

00:03:20.877 --> 00:03:23.849
But the mean will change, if
this becomes really, really

00:03:23.849 --> 00:03:27.121
astronomically high it
will distort the actual

00:03:27.121 --> 00:03:29.285
mean here, actually could
distort it a good bit.

00:03:29.285 --> 00:03:32.689
So for geology majors
from UNC the median income

00:03:32.689 --> 00:03:34.800
is going to be lower than the mean because

00:03:34.800 --> 00:03:37.831
Michael Jordan is pulling the mean up.

00:03:37.831 --> 00:03:39.562
So let me fill that in.

00:03:39.562 --> 00:03:41.873
"So for geology majors
from UNC, the median

00:03:41.873 --> 00:03:43.945
"will be less than the mean."

00:03:43.945 --> 00:03:45.653
Now let's think about the other ones,

00:03:45.653 --> 00:03:47.873
"For civil engineering
majors from Montana,

00:03:47.873 --> 00:03:50.352
"the median income will
be" blank "the mean."

00:03:50.352 --> 00:03:53.345
Well they tell us there were
only three civil engineering

00:03:53.345 --> 00:03:55.569
majors from the University of Montana.

00:03:55.569 --> 00:03:58.161
They all took the exact
same job at the same company

00:03:58.161 --> 00:04:00.000
earning the same salary.

00:04:00.000 --> 00:04:02.859
So let's say all 3 of them
earn 50 thousand dollars.

00:04:02.859 --> 00:04:05.244
Let's say that's their salary so you have

00:04:05.244 --> 00:04:08.145
if you were to calculate
the mean it would be

00:04:08.145 --> 00:04:13.809
50 + 50 + 50 over 3 which of course is 50.

00:04:13.809 --> 00:04:15.071
That would be the mean.

00:04:15.071 --> 00:04:18.623
If you wanted the median you
list the salaries in order

00:04:18.623 --> 00:04:20.649
and then you take the middle
one, well the middle one

00:04:20.649 --> 00:04:25.336
is 50, so in this case the
median is equal to the mean.

00:04:25.520 --> 00:04:28.823
So let's fill that in,
median is equal to the mean.

00:04:28.823 --> 00:04:32.532
And then finally, wait let
me go back to my scratchpad.

00:04:32.532 --> 00:04:35.809
Whoops, let me go back
to my scratchpad here.

00:04:35.809 --> 00:04:39.113
"For finance majors from
Wesleyan, the median income

00:04:39.113 --> 00:04:41.145
will be," blank "the mean."

00:04:41.145 --> 00:04:43.659
So let's think about
this distribution here.

00:04:43.659 --> 00:04:47.313
So here we have 35, out of
the 35, 32 got high-paying

00:04:47.313 --> 00:04:51.374
consulting jobs so let's
say that they were making

00:04:51.374 --> 00:04:55.673
six-figures so the distribution might look

00:04:55.673 --> 00:05:00.351
something like this, this
is 0 and this is let's say

00:05:00.351 --> 00:05:04.618
this is 50K and let's say
that this right over here

00:05:04.618 --> 00:05:07.297
is 100 thousand dollars a years.

00:05:07.297 --> 00:05:09.606
So 32 got high-paying consulting jobs,

00:05:09.606 --> 00:05:17.113
so you might have 1, 2,
3, 4, 5, 6, 7, 8, 9, 10,

00:05:17.113 --> 00:05:24.148
11, 12, 13, 14, 15, 16,
17, 18, 19, 20, 21, 22,

00:05:24.148 --> 00:05:33.191
23, 24, 25, 26, 27, 28, 29, 30, 31, 32.

00:05:33.191 --> 00:05:35.786
So the distribution for
the people who got the jobs

00:05:35.786 --> 00:05:38.245
might look something
like that but there were

00:05:38.245 --> 00:05:40.668
3 people who are unemployed
so let's say they

00:05:40.668 --> 00:05:45.028
got no income, so you have 1, 2, 3.

00:05:45.551 --> 00:05:48.426
So this is now, you have 3
outliers like the Michael

00:05:48.426 --> 00:05:50.981
Jordan situation but instead
of them being very high

00:05:50.981 --> 00:05:54.131
they are very low so they're
going to pull the mean

00:05:54.131 --> 00:05:56.737
lower, they're not going
to, if these were 0

00:05:56.737 --> 00:05:59.409
or these were 50, or these were over here,

00:05:59.409 --> 00:06:01.737
they're not going to affect the median.

00:06:01.737 --> 00:06:03.804
The middle number is still
going to be the same.

00:06:03.804 --> 00:06:06.097
But they are going to pull down the mean.

00:06:06.097 --> 00:06:08.788
So here I would say that
the median income will

00:06:08.788 --> 00:06:13.466
likely be higher, will likely
be greater than the mean.

00:06:13.466 --> 00:06:15.557
Because the mean is
going to get pulled down

00:06:15.557 --> 00:06:18.431
by these outliers, these three
people not make anything.

00:06:18.431 --> 00:06:20.401
So let's fill that out.

00:06:20.401 --> 00:06:22.497
"For finance majors from
Wesleyan, the median income

00:06:22.497 --> 00:06:25.631
"will likely be greater than the mean."

00:06:25.631 --> 23:59:59.999
Now let's check our answer,
and we got it right.


Statistical significance of experiment

WEBVTT
Kind: captions
Language: en

00:00:00.388 --> 00:00:02.116
Voiceover:In an experiment
aimed at studying

00:00:02.116 --> 00:00:05.376
the effect of advertising on
eating behavior in children,

00:00:05.376 --> 00:00:08.697
a group of 500 children,
seven to 11 years old

00:00:08.697 --> 00:00:10.918
were randomly assigned
to two different groups.

00:00:10.918 --> 00:00:13.664
After randomization, each child was asked

00:00:13.664 --> 00:00:15.354
to watch a cartoon in a private room,

00:00:15.354 --> 00:00:18.903
containing a large bowl
of goldfish crackers.

00:00:18.903 --> 00:00:21.853
The cartoon included
two commercial breaks.

00:00:21.853 --> 00:00:24.237
The first group watched food commercials,

00:00:24.237 --> 00:00:26.648
mostly snacks while the second group

00:00:26.648 --> 00:00:28.142
watched non-food commercials,

00:00:28.142 --> 00:00:29.744
games and entertainment products.

00:00:29.744 --> 00:00:32.352
Once the child finished
watching the cartoon,

00:00:32.352 --> 00:00:35.413
the conductors of the experiment
weighed the cracker bowls

00:00:35.413 --> 00:00:38.238
to measure how many grams
of crackers the child ate.

00:00:38.238 --> 00:00:40.533
They found that the
mean amount of crackers

00:00:40.533 --> 00:00:43.149
eaten by the children who
watched food commercials

00:00:43.149 --> 00:00:46.571
is 10 grams greater than
the mean amount of crackers

00:00:46.571 --> 00:00:49.370
eaten by the children who
watched non-food commercials.

00:00:49.370 --> 00:00:52.472
Let's just think about what
happens up to this point.

00:00:52.472 --> 00:00:56.731
They took 500 children

00:00:56.731 --> 00:00:58.690
and then they randomly assigned them

00:00:58.690 --> 00:01:00.300
to two different groups.

00:01:00.300 --> 00:01:02.083
You have group one over here

00:01:02.083 --> 00:01:03.871
and you have group two.

00:01:03.871 --> 00:01:06.473
Let's say that this right
over here is the first group.

00:01:06.473 --> 00:01:08.791
The first group watched food commercials.

00:01:08.791 --> 00:01:11.009
This is group number one.

00:01:11.009 --> 00:01:13.150
They watched food commercials.

00:01:13.150 --> 00:01:15.164
We could call this the treatment group.

00:01:15.164 --> 00:01:16.459
We're trying to see what's the effect

00:01:16.459 --> 00:01:19.603
of watching food commercials
and then they tell us.

00:01:19.603 --> 00:01:24.129
The second group watched
non-food commercials,

00:01:24.129 --> 00:01:25.606
so this is the control group.

00:01:25.606 --> 00:01:29.931
Number two, this is non-food commercials.

00:01:29.931 --> 00:01:33.854
This is the control right over here.

00:01:33.854 --> 00:01:36.508
Once the child finished
watching the cartoon,

00:01:39.184 --> 00:01:40.742
for each child they weighed

00:01:40.742 --> 00:01:42.262
how much of the crackers they ate

00:01:42.262 --> 00:01:44.343
and then they took the mean of it

00:01:44.343 --> 00:01:46.446
and they found that the mean here

00:01:46.446 --> 00:01:49.074
that the kids ate 10
grams greater on average

00:01:49.074 --> 00:01:51.100
than this group right over here

00:01:51.100 --> 00:01:53.797
which just looking at that
data makes you believe

00:01:53.797 --> 00:01:56.743
that okay, well something
maybe happened over here.

00:01:56.743 --> 00:01:59.422
That maybe the treatment from
watching the food commercials

00:01:59.422 --> 00:02:04.343
made the students eat more
of the goldfish crackers

00:02:04.343 --> 00:02:06.783
but the question that you
always have to ask yourself

00:02:06.783 --> 00:02:07.969
in a situation like this.

00:02:07.969 --> 00:02:09.643
Well, isn't there some probability

00:02:09.643 --> 00:02:11.255
that this would have happened by chance

00:02:11.255 --> 00:02:14.510
that even if you didn't make
them watch the commercials.

00:02:14.510 --> 00:02:16.644
If these were just two random groups

00:02:16.644 --> 00:02:18.946
and you didn't make either
group watch a commercial,

00:02:18.946 --> 00:02:20.504
you made them all watch
the same commercials.

00:02:20.504 --> 00:02:23.527
There's some chance that
the mean of one group

00:02:23.527 --> 00:02:25.694
could be dramatically
different than the other one.

00:02:25.694 --> 00:02:27.782
It just happened to be in this experiment

00:02:27.782 --> 00:02:30.321
that the mean here that it looks like

00:02:30.321 --> 00:02:32.015
the kids ate 10 grams more.

00:02:32.015 --> 00:02:34.360
How do you figure out,
what's the probability

00:02:34.360 --> 00:02:36.171
that this could have happened,

00:02:36.171 --> 00:02:40.752
that the 10 grams greater
in mean amount eaten here

00:02:40.752 --> 00:02:42.734
that that could have
just happened by chance.

00:02:42.734 --> 00:02:45.909
Well the way you do it is
what they do right over here.

00:02:45.909 --> 00:02:52.557
Using a simulator, they
re-randomize the results

00:02:52.557 --> 00:02:55.170
into two new groups and
measure the difference

00:02:55.170 --> 00:02:57.076
between the means of the new groups.

00:02:57.076 --> 00:02:59.477
They repeated the simulation 150 times

00:02:59.477 --> 00:03:01.493
and plotted the differences given.

00:03:01.493 --> 00:03:04.449
The resulting difference
is as given below.

00:03:04.449 --> 00:03:07.500
What they did is they said, okay,

00:03:07.500 --> 00:03:11.322
they have 500 kids and each
kid, they had 500 children.

00:03:11.322 --> 00:03:17.201
Number one, two, three,
all the way up to 500.

00:03:17.924 --> 00:03:19.550
For each child they measured

00:03:19.550 --> 00:03:22.879
how much was the weight of
the crackers that they ate?

00:03:22.879 --> 00:03:25.127
Maybe child one ate two grams

00:03:25.127 --> 00:03:27.737
and child two ate four grams

00:03:27.737 --> 00:03:32.695
and child three ate, I
don't know, ate 12 grams

00:03:32.695 --> 00:03:35.559
all the way to child number 500 ate,

00:03:35.559 --> 00:03:37.378
I don't know, maybe they
didn't eat anything at all,

00:03:37.378 --> 00:03:38.474
ate zero grams.

00:03:38.474 --> 00:03:41.553
We already know, let's
say the first time around.

00:03:46.135 --> 00:03:50.450
The first half was in the treatment group

00:03:50.450 --> 00:03:54.438
when we're just ranking them like this

00:03:54.438 --> 00:03:56.348
and then the second,
they're randomly assigned

00:03:56.348 --> 00:03:58.551
into these groups and at the second half

00:03:58.551 --> 00:04:01.272
was in the control group.

00:04:01.272 --> 00:04:03.080
What they're doing now

00:04:03.080 --> 00:04:04.591
is they're taking the same results

00:04:04.591 --> 00:04:06.058
and they're re-randomizing it.

00:04:06.058 --> 00:04:07.104
Now they're saying, okay,

00:04:07.104 --> 00:04:11.393
let's maybe put this
person in group number two

00:04:11.393 --> 00:04:14.859
and this person in group number two

00:04:14.859 --> 00:04:17.576
and this person stays in group number two

00:04:17.576 --> 00:04:20.328
and this person stays in group number one

00:04:20.328 --> 00:04:22.434
and this person stays in group number one.

00:04:22.434 --> 00:04:24.252
Now they're completely mixing up

00:04:24.252 --> 00:04:25.808
all of the results that they had.

00:04:25.808 --> 00:04:28.624
It's completely random
of whether the student

00:04:28.624 --> 00:04:30.271
had watched the food commercial

00:04:30.271 --> 00:04:31.514
or the non-food commercial

00:04:31.514 --> 00:04:34.915
and then they're testing what's the mean

00:04:34.915 --> 00:04:37.999
of the new number one group
and the new number two group.

00:04:37.999 --> 00:04:41.033
They're saying well,
what is the distribution

00:04:41.033 --> 00:04:42.819
of the differences in means.

00:04:42.819 --> 00:04:45.181
They see when they did this way

00:04:45.181 --> 00:04:47.025
when they're essentially
just completely randomly

00:04:47.025 --> 00:04:49.968
taking these results and putting
them into two new buckets.

00:04:49.968 --> 00:04:51.759
You have a bunch of cases

00:04:51.759 --> 00:04:53.881
where you get no difference in the means.

00:04:53.881 --> 00:04:58.678
Out of the 150 times that
they repeated the simulation

00:04:58.678 --> 00:05:01.248
doing this little exercise here.

00:05:01.248 --> 00:05:05.062
One, two, three, four, five,
six, seven, eight, nine,

00:05:05.062 --> 00:05:07.923
10, 11, 12, 13, 14, 15.

00:05:07.923 --> 00:05:09.356
I'm having trouble
counting this let's see.

00:05:09.356 --> 00:05:13.628
One, two, three, four, five,
six, seven, eight, nine,

00:05:13.628 --> 00:05:14.961
10, 11, 12.

00:05:14.961 --> 00:05:19.468
It's so small, I'm aging

00:05:19.468 --> 00:05:21.836
but it looks like there's
about, I don't know.

00:05:21.836 --> 00:05:23.519
High teens about 20 times

00:05:23.519 --> 00:05:26.590
when there's actually
no noticeable difference

00:05:26.590 --> 00:05:27.827
in the means of the groups

00:05:27.827 --> 00:05:31.416
where you just randomly
allocate the results

00:05:31.416 --> 00:05:32.757
amongst the two groups.

00:05:32.757 --> 00:05:34.781
When you look at this, if it was just,

00:05:34.781 --> 00:05:37.330
if you just randomly put
people into two groups,

00:05:37.330 --> 00:05:41.207
the probability or the situations

00:05:41.207 --> 00:05:46.966
where you get a 10 gram difference

00:05:46.966 --> 00:05:49.152
are actually very unlikely.

00:05:50.321 --> 00:05:51.923
Let's see, is this the difference?

00:05:51.923 --> 00:05:53.984
The difference between the
means of the new groups.

00:05:53.984 --> 00:05:57.090
It's not clear whether this
is group one minus group two

00:05:57.090 --> 00:05:59.265
or group two minus group one

00:05:59.265 --> 00:06:02.074
but in either case the situations

00:06:02.074 --> 00:06:06.518
where you have a 10
gram difference in mean.

00:06:06.518 --> 00:06:10.161
It's only two out of the 150 times.

00:06:10.161 --> 00:06:12.097
When you do it randomly,

00:06:12.097 --> 00:06:14.969
when you just randomly put these results

00:06:14.969 --> 00:06:15.956
into two groups,

00:06:15.956 --> 00:06:18.507
the probability of the
means being this different,

00:06:18.507 --> 00:06:22.210
it only happens two out of the 150 times.

00:06:22.210 --> 00:06:23.498
There's a 150 dots here.

00:06:23.498 --> 00:06:30.129
That is on the order of 2% or
actually it's less than 2%,

00:06:30.129 --> 00:06:31.569
it's between one and 2%.

00:06:31.569 --> 00:06:35.807
Let's say the situation
we're talking about.

00:06:35.807 --> 00:06:38.802
Let's say that this is
group one minus group two

00:06:38.802 --> 00:06:40.153
in terms of how much was eaten

00:06:40.153 --> 00:06:42.053
and so you're looking at this
situation right over here

00:06:42.053 --> 00:06:44.698
that that's only one out of a 150 times.

00:06:44.698 --> 00:06:50.608
It happened less frequently
than one in a 100 times.

00:06:50.608 --> 00:06:53.468
It happened only one in a 150 times.

00:06:53.468 --> 00:06:55.709
If you look at that, you
say well, the probability

00:06:55.709 --> 00:06:56.800
this was just random.

00:06:56.800 --> 00:06:58.658
The probability of getting
the results that you got

00:06:58.658 --> 00:07:00.592
is less than 1%.

00:07:00.592 --> 00:07:03.858
To me and then to most statisticians,

00:07:03.858 --> 00:07:06.593
that tells us that our
experiment was significant,

00:07:06.593 --> 00:07:09.256
that the probability of getting
the results that you got.

00:07:09.256 --> 00:07:11.218
The children who watched food commercials

00:07:11.218 --> 00:07:13.155
being 10 grams greater
than the mean amount

00:07:13.155 --> 00:07:14.434
of crackers eaten by the children

00:07:14.434 --> 00:07:15.743
who watched non-food commercials.

00:07:15.743 --> 00:07:18.100
If you just randomly put 500 kids

00:07:18.100 --> 00:07:20.610
into two different buckets
based on the simulation results

00:07:20.610 --> 00:07:23.522
it looks like there's only,

00:07:23.522 --> 00:07:25.582
if you'd run the simulation a 150 times,

00:07:25.582 --> 00:07:27.994
that only happened one
out of the 150 times.

00:07:27.994 --> 00:07:31.557
It seems like this was
very, it's very unlikely

00:07:31.557 --> 00:07:33.131
that this was purely due to chance.

00:07:33.131 --> 00:07:35.579
If this was just a chance event,

00:07:35.579 --> 00:07:38.953
this would only happen
roughly one in 150 times

00:07:38.953 --> 00:07:40.698
but the fact that this
happened in your experiment,

00:07:40.698 --> 00:07:42.725
it makes you feel pretty confident

00:07:42.725 --> 00:07:44.576
that your experiment is significant.

00:07:44.576 --> 00:07:47.593
In most studies, in most experiments,

00:07:47.593 --> 00:07:49.311
the threshold that they think about

00:07:49.311 --> 00:07:53.593
is the probability of something
statistically significant.

00:07:53.593 --> 00:07:56.321
If the probability of
that happening by chance

00:07:56.321 --> 00:07:59.902
is less than 5%, this is less than 1%.

00:07:59.902 --> 00:08:02.764
I would definitely say that
the experiment is significant.