Given the following information about a hypothesis test of the difference between two means based on independent random samples, which one of the following is the correct rejection region at a significance level of .05? Assume that the samples are obtained from normally distributed populations having equal variances.

Question

H0: μA ≤ μB, H1: μA >μB 1 = 12, 2 = 9, s1 = 4, s2=2, n1 = 13, n2 = 10.

A. Reject H0 if Z > 1.96
B. Reject H0 if Z > 1.645
C. Reject H0 if t > 2.08
D. Reject H0 if t > 1.782

Answer 1

I'll give you a hint.

H1 tells you if the test is one-tailed or two-tailed. If H1 shows a specific direction, like > or <, then the test is one-tailed. If the test does not show a specific direction, then the test is two-tailed. Therefore, since H1 shows a specific direction, look at the appropriate table for a one-tailed test at .05 level of significance.

I'll let you take it from here.