Assume that you have a sample of $n_1 = 7$, with the sample mean $\bar{X}_1 = 50$, and a sample standard deviation of $S_1 = 4$, and you have an independent sample of $n_2 = 13$ from another population with a sample mean of $\bar{X}_2 = 36$ and the sample standard deviation $S_2 = 8$. Complete parts (a) through (d) below.
a. What is the value of the pooled-variance $t_{STAT}$ test statistic for testing $H_0: \mu_1 = \mu_2$?
$t_{STAT} = $
(Round to two decimal places as needed.)
b. In finding the critical value, how many degrees of freedom are there?
degrees of freedom
(Simplify your answer.)
c. Using a significance level of $\alpha = 0.01$, what is the critical value for a one-tail test of the hypothesis $H_0: \mu_1 \le \mu_2$ against the alternative $H_1: \mu_1 > \mu_2$?
The critical value is
(Round to two decimal places as needed.)
d. What is your statistical decision?
OA. Do not reject $H_0$ because the computed $t_{STAT}$ test statistic is greater than the upper-tail critical value.
OB. Reject $H_0$ because the computed $t_{STAT}$ test statistic is less than the upper-tail critical value.
OC. Do not reject $H_0$ because the computed $t_{STAT}$ test statistic is less than the upper-tail critical value.
OD. Reject $H_0$ because the computed $t_{STAT}$ test statistic is greater than the upper-tail critical value.