Two independent samples have been selected, $60$ observations from population 1 and $79$ observations from population 2. The sample means have been calculated to be $\overline{x}_1 = 6.8$ and $\overline{x}_2 = 12.9$. From previous experience with these populations, it is known that the variances are $\sigma_1^2 = 40$ and $\sigma_2^2 = 31$.

(a) $\ $ Find $\sigma_{(\overline{x}_1 - \overline{x}_2)}$.
answer:

(b) $\ $ Determine the rejection region for the test of $H_0:(\mu_1 - \mu_2) = 2.44$ and $H_a:(\mu_1 - \mu_2) > 2.44$ Use $\alpha = 0.04$.
$z >$

(c) $\ $ Compute the test statistic.
$z =$

The final conclustion is

A. We can reject the null hypothesis that $(\mu_1 - \mu_2) = 2.44$ and accept that $(\mu_1 - \mu_2) > 2.44$.
B. There is not sufficient evidence to reject the null hypothesis that $(\mu_1 - \mu_2) = 2.44$.

(d) $\ $ Construct a $96$ % confidence interval for $(\mu_1 - \mu_2)$.
$\leq (\mu_1 - \mu_2) \leq$