Question

Publisher is interested in the effects of sales of college texts that include more than 100 data files. The Publisher plans to produce 20 texts in the business area and randomly chooses 10 to have more than 100 fileas. The remaining 10 are produced with at most 100 files. For those with mıre than 100, first-year sales averaged 9254 and the sampel standard deviation was 2107. Fort he boks with at most 100 files, average first-year sales were 8167, and sample standard deviation was 1681. Assuming the two population distributions are normal, test the null hypothesis that the population variances are equal against the alternative that the population variance is higher for books with more than 100 files.

For this problem clearly state the

a) null and alternative hypothesis,

b) decision rule and

c) conclusion.

Answer 1

The sample variances are and and the sample sizes are given by n1​=10 and n2​=10.

(1) Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

This corresponds to a right-tailed test, for which a F-test for two population variances needs to be used.

(2) Rejection Region

The significance level is α=0.05, and the rejection region for this right-tailed test is R = { F : F > FU ​=3.179}.

(3) Test Statistics

The F-statistic is computed as follows:

(4) Decision about the null hypothesis

Since from the sample information we get that F = 1.253 ≤ FU ​= 3.179, it is then concluded that the null hypothesis is not rejected.

(5) Conclusion

It is concluded that the null hypothesis Ho is not rejected. Therefore, there is not enough evidence to claim that the population variance ​ is greater than the population variance , at the α=0.05 significance level.

Therefore, there is not enough evidence to claim that population variance is higher for books with more than 100 files.