00:01
This question talks about two identical surveys that were taken a month apart and asks if there is a significant difference between them.
00:09
The first, well, so first what we need is a null hypothesis.
00:13
This is going to be a hypothesis test, and so we need a null hypothesis to test against.
00:20
The null is going to be that nothing changed.
00:23
That's what we don't have any evidence to suggest that something did change.
00:27
So a skeptic would believe that nothing probably changed.
00:31
So we're just going to stick with the same proportions.
00:36
So that means that our null hypothesis will be in the new survey, the survey that was taken in october, the proportions will be the same as what was taken in september.
00:48
So to write this out, we'll have that the probability of someone saying that health care requirements are getting better after the bill will be 0 .22.
01:00
Probability of people saying that they will not share change, p of n, i'll call it, is going to be 0 .35.
01:08
A proportion of people saying that they'll get worse, p of w is going to be 0 .38, and the proportion of people who are unsure will be 0 .05, 5%.
01:22
So this is our null hypothesis.
01:24
And so let's do a hypothesis test on this.
01:27
We know that this is a multinomial experiment.
01:30
We have four categories.
01:31
So we're going to be using a kai squared test statistic.
01:35
For kai squared, of course, we know we need observed and expected values.
01:41
We'll be able to figure out our expected values, but let's take a look first at our observed values.
01:45
The observed values are going to be the values that we found in the survey taken in october.
01:50
So this is the survey that we're testing.
01:53
We found that 380 said that they would get better.
01:58
380 also said that they would stay the same, no change.
02:01
700 say that they would get worse.
02:03
And 61 said that they would not.
02:06
They were unsure.
02:08
So these are our observed values.
02:09
Now, what are our expected values? well, the expected values are going to be the null probabilities, what we just wrote up here, times the sample size.
02:20
And here the sample size is 1 ,521.
02:24
That's how many people were surveyed in the october survey.
02:28
So with 1 ,521 people, we'd multiply that by each.
02:34
Of our null probabilities and we'll get the our expected values.
02:39
So i'm going to do that now.
02:41
0 .22 times 1521 is going to be 3334 .62.
02:50
0 .35 times 1521 is going to be 532 .35.
03:00
We'll have 38 % of 1521, which is 577.
03:06
0 .98 and we'll have 5 % of 1 ,521, which is just 226, no, excuse me, 76, getting ahead of myself, 76 .5.
03:23
So now we need to find the difference, and we need to find not just the difference, the difference, squared.
03:30
So we're going to find o minus e squared because this is a part of our kai squared statistic.
03:37
So i'm going to do this actually just in a calculator.
03:41
These are pretty big numbers that we're working with...