00:01
For this question, you're looking at a chi -squared test, basically.
00:07
A researcher wonders if there's a link between gender and political party.
00:11
He takes a random sample of 179 people.
00:14
119 are men, 60 are women, 53 are democrats, 34 are which are men, 25 are republicans, 5 of which are women, and the rest are independents.
00:27
We're going to use a test and appropriate hypothesis at an alpha level of 0 .01.
00:35
So, first what we need to do is create a table of all this data.
00:42
What we're going to wind up doing is doing this and finding our expected counts table, and then we're going to find out this little table that contributes to the test statistic.
00:54
You have to do this, and once you do this on part b, you just add them all together to get that test statistic.
01:01
So here's what we're going to do.
01:03
First, you have to come up with a table, and we need one that looks pretty much just like this.
01:09
So, it needs to be...
01:19
Okay, this is down to male, female, republican, independent, and we're going to have totals for these rows and totals for these columns.
01:40
So, let's see.
01:44
How many male democrats do we have? when we went through this, it determined that 53 democrats, 34 were men.
01:55
So, 34 goes right here in this spot.
01:59
So, if 34 were men, then 53 minus 34 is 19.
02:10
19 females.
02:16
And that gives us a total of 53 democrats.
02:27
Republicans, it says there was 25 republicans, and it says here that 5 are women.
02:36
5 of them are women, so that means 20 of them had to be men, and the rest of them were independents.
02:44
So, of the 119 men, 34 of them were democrats, 20 of them were republicans.
02:56
Let's just take away the two parties, and we get a total of 65 independents.
03:03
60 of them were women, so if you take your 60 women minus the 19 democrats minus the 5 republicans, you get 36.
03:16
So, for a total, 65 plus 36, you get 101.
03:23
And if we do our column totals here, well, men, there should have been 119, and then females, there should have been 60.
03:34
For a grand total of 179.
03:40
If we add this way, we get 179.
03:42
If we add this way, we get 179.
03:47
So, we've got our little table here.
03:49
Now, to get these expected counts, to get those expected counts, we want...
03:58
I'm going to go ahead and just run through it and make sure i get the number here.
04:01
So, let's just run through this and make sure we can get that number.
04:04
If i want that number for democrat males, that's in this spot, so i'm going to take this total from that row and this total here from this column.
04:20
If i recall correctly, i think we'll take those two numbers and we'll divide it by the total, 179.
04:32
So, 53 times 119 divided by 179 equals 35 .234.
04:43
35 .234, oh, it's rounded to 2 .5.
04:46
Awesome.
04:47
So, we got that.
04:50
So, all i did was take the row and the column that the democrat men were in, multiply them, divide by the grand total.
05:00
So, it wants the female spot now here.
05:02
It wants female democrats.
05:07
So, let's take off this blue highlight.
05:09
It might confuse us if it's still there.
05:14
And what we're wanting now is this to fill in this spot of our table.
05:20
So, we're going to use the total, row total of 5 and the row total of 60.
05:27
We'll multiply those two numbers together, divide by the 179, and we get 1.
05:38
I'm going to run out of three decimal places.
05:43
1 .676 would be that little number there.
05:49
Now, when we want to find the contributions to the test statistic, what you do to find your chi -squared test statistic is you would take my, i would take the observed count, the observed minus the expected.
06:10
So, i subtract those two numbers.
06:13
I square it and then divide by the expected number.
06:19
And then you do that process for all of them...