Given the following information about a hypothesis test of the difference between two means based on independent random samples from two normally distributed populations with unknown but equal variances,which one of the following is the correct rejection region at a significance level of .05?
H_A: ?_A > ?_B, $\bar { X }$
₁ = 12, $\bar { X }$
₂ = 9,s₁ = 3,s₂ = 2,n₁ = 13,n₂ = 10.

Question

Given the following information about a hypothesis test of the difference between two means based on independent random samples from two normally distributed populations with unknown but equal variances,which one of the following is the correct rejection region at a significance level of .05?
H_A: ?_A > ?_B,

\bar { X }

₁ = 12,

\bar { X }

₂ = 9,s₁ = 3,s₂ = 2,n₁ = 13,n₂ = 10.

Quizplus · Accepted Answer

The correct rejection region is C) Reject H0 if t > 1.721. This is because the test statistic for this hypothesis test is a t-statistic, and the critical value for a two-tailed test with a significance level of .05 and degrees of freedom equal to 21 (n1 + n2 - 2) is 1.721.

Given the Following Information About a Hypothesis Test of the Difference