00:01
And i'll start to help you on some of these.
00:02
So in your first one, you have that you have the four proportions you're going to assume for this setting are equal to 0 .25.
00:14
And your categories are you have frequencies of, well, let's do it this way.
00:20
You have frequencies for your categories of 85, 58, 89, and 75.
00:29
And your appropriate alternative hypotheses would be that not all proportions equal 0 .25.
00:45
You're not saying they're all wrong.
00:48
Next, you want to calculate the test statistic.
00:50
Well, we need to find what the sum of this is.
00:53
It shows you that you would have had, these are supposed to add up to 307.
00:57
So if we take 307 divided by 4, that means our expected values are 76 .75 for each of these.
01:09
And those are our expected values.
01:11
So this is a chi -squared test.
01:14
And i'm going to enter in my calculator those observed values in list one.
01:21
So i'll put that 85, 58, 89, and 72.
01:28
And then my 76 .75 is going to be my expected value for each of these.
01:37
And we'll perform a chi -squared goodness of fit test.
01:41
And we know we can calculate it out longhand.
01:43
But that test statistic you need to at least four decimal places and a final answer.
01:49
So and again, i'm not going to show the work on this.
01:52
I'm just going to compute that.
01:54
We know we take the difference between the numbers squared divided by the expected.
01:58
And again, it is a goodness of fit test.
02:02
And i have my data in list one and list two.
02:04
I do have to say that my degrees of freedom is three.
02:08
I'm not sure why the software doesn't just automatically figure that.
02:11
But 7 .7166 is to four decimal places.
02:16
Now part c, oh, we have to give the p -value.
02:21
And the p -value for this setting is actually 0 .0522.
02:26
So you can see that the p -value is between 0 .05 and 0 .10.
02:36
Now part c asks you to look at a 10 % significance level.
02:42
What is your decision? we would reject the null since the p -value is less than that 0 .10...