Chapter 10, Problem 2PS

Assume that you have a sample of $n{1}_{}=8,$ with the sample mean ${\bar{X}}_1=42,$ and a sample standard deviation $S_1=4,$ and you have an independent sample $n_2=15$ from another population with a sample of $n_2=15$ from another population with a sample ${\bar{X}}_2=34$ and a sample standard deviation $S_2=5.$

a. What is the value of the pooled-variance $t_{STAT}$ test statistic for testing $H_0:{\mu }_1={\mu }_2?$

b. In finding the critical value, how many degrees of freedom are there?

c. Using the level of significance $\alpha =0.01,$ what is the critical value for a one-tail test of the hypothesis $H_0:{\mu }_1\le {\mu }_2$ against the alternative, $H_1:{\mu }_1>{\mu }_2?$

d. What is your statistical decision?