Chapter 11, Problem 8E

For Exercises 7 and 8: (a) state the decision rule, (b) compute the pooled estimate of the population variance, (c) compute the test statistic, (d) state your decision about the null hypothesis, and (e) estimate the p-value.

8. The null and alternate hypotheses are:

$\begin{array}{c}{H}_0:{\text{μ}}_{\text{1}}={\text{μ}}_{\text{2}}\\ H_1:{\text{μ}}_{\text{1}}\ne {\text{μ}}_{\text{2}}\end{array}$

A random sample of 15 observations from the first population revealed a sample mean of 350 and a sample standard deviation of 12. A random sample of 17 observations from the second population revealed a sample mean of 342 and a sample standard deviation of 15. At the .10 significance level, is there a difference in the population means?