00:01
So in the following question, we have been given a scores from eight sample exams.
00:07
So our sample size is eight.
00:11
And we have been given that the variance of exam scores before these eight scores was 4 .652.
00:24
So let's just say sigma not square is 4 .652.
00:36
And we're supposed to confirm or deny the claim stated by the professor using an appropriate test and we're supposed to find the value of this test statistic.
00:51
So data, i'm just going to write down the points over here really quick.
00:56
So 42, 41, 45, 49, 43, 47, and 41.
01:08
All right i missed a 40 right in the middle because there were eight data points so this is 40 47 and 41 all right so since we're supposed to confirm or deny the variance value we can use a kai square test because we normally use a kai square pierce in kai square test to determine whether or not the variance mentioned is a true variance of the mean or of the sample or not.
02:06
So i'm going to say our null hypothesis, just going to write it as null hype is h0.
02:21
So null hypothesis h0 is that the variance is indeed, equal to sigma not square.
02:37
And the alternate hypothesis is that the variance is not equal to sigma not square.
02:46
And the test statistic, let's just call that t.
02:51
I have the formula for that right here, which i'm going to write down...