Chapter 11, Problem 13E

For exercises 13 and 14, assume the sample populations do not have equal standard deviations and use the .05 significance level: (a) determine the number of degrees of freedom, (b) state the decision rule, (c) compute the value of the test statistic, and (d) state your decision about the null hypothesis.

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 items from the first population showed a mean of 50 and a standard deviation of 5. A sample of 12 items for the second population showed a mean of 46 and a standard deviation of 15.