A publisher is interested in the effects on sales of college texts of expensive three-colour cover designs. The publisher is planning to bring out 20 texts in the business area and randomly chooses 10 of them to have expensive cover designs. The remaining 10 are produced with plain covers. For those with expensive cover designs, first-year sales averaged $ 9294 and the sample standard deviation was $ 2001. For the books with plain cover designs, first-year sales averaged $ 8668 and the sample standard deviation was $ 1700.

(a) Assuming that the two population distributions are normal with the same variance, test the null hypothesis that the population means are equal against the alternative that the true mean is higher for books with expensive cover designs. Use a 5% significance level. Answer the following, and round off your answer to three decimal places.

(i) Find a pooled estimate of the population standard deviation.

(ii) What is the test statistic used in the decision rule?

(iii) What is the critical value?

(iv) What decision do you make? A. Reject the null hypothesis.

B. Do not reject the null hypothesis.

(b) In (a), it was assumed that population variances were equal for first-year sales of textbooks with plain and expensive cover designs. Test this assumption against a two-sided alternative. Use a 10% significance level. (i) What is the test statistic?

(ii) What decision do you make?

A. Reject the null hypothesis.

B. Do not reject the null hypothesis.