Question

Two college instructors are interested in whether or not there is any variation in the way they grade math exams. They each grade the same set of 12 exams. The first instructor's grades have a variance of 52.3. The second instructor's grades have a variance of 89.9. Test the claim that the first instructor's variance is smaller. The level of significance is 5%.

Answer 1

H0: first instructor variace = 2nd instructor variance

Ha: first instructor variace < 2nd instructor variance

First instructor variance =52.3

Second instructor variance =89.9

Test statistic, F= 89.9/52.3 =1.72

n=12=n1=n2

Critical value = F_0.05,11,11 = 2.82

Since, test statistic is less than critical value, so fail to reject null hypothesis. There is not enough evidence to reject null hypothesis.

First instructor variance = second instructor variance.

So the claim is not true.

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