1.We wish to compare the variances of two populations.We take random samples from each with the following results:

Sample 1: n = 20,sample standard deviation = 25.5

Sample 2:n = 30,sample standard deviation = 16.1

We wish to use the F test to test whether the population standard deviations are equal.

a.What are the hypotheses for a 1-sided F test?

Ho: Variance 1 / Variance 2 = 1

Ha: Variance 1 / Variance 2 > 1

b.What is the F statistic for this test?

25.5 / 16.1 = 1.58

c.What are the degrees of freedom (numerator and denominator) for this test?

Numerator = 20 - 1 =19

Denominator = 30 - 1 = 29

d.The critical value for a 1-sided F test based on these samples at = 0.10 is 1.685.Given this and assuming a valid test, state the conclusion of this test.

The F statistic(1.58) is less than the critical value(1.685), so we fail to reject the null. Therefore, the population variance 1 is greater than population variance 2.