Chapter 9.3, Problem 26BB

Pooling. In Exercises 25 and 26, assume that the two samples are independent simple random samples selected from normally distributed populations. Also assume that the population standard deviations are equal (σ₁ = σ₂), so that the standard error of the differences between means is obtained by pooling the sample variances as described in Part 2 of this section.

26. Do Men Talk Less Than Women? Repeat Exercise 8 with the additional assumption that σ₁ = σ₂. How arc the results affected by this additional assumption?

8. Do Men Talk Less Than Women? The accompanying table gives results from a study of the words spoken in a day by men and women, and the original data are in Data Set 17 in Appendix B (based on “Are Women Really More Talkative Than Men?” by Mehl, et al., Science, Vol. 317, No. 5834). Use a 0.01 significance level to test the claim that the mean number of words spoken in a day by men is less than that for women.

Table for Exercise 8

Men		Women
n1 =	186	n2 = 210
${\bar{x}}_1$ =	15,668.5	${\bar{x}}_2$ = 16,215.0
s1 =	8632.5	s2 = 7301.2