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? H_A: µ_A µ_B, 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 1.721 D)Reject H₀ if t 2.08 E)Reject H₀ if t 1.782

Question

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? H_A: µ_A> µ_B, 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 > 1.721 D)Reject H₀ if t > 2.08 E)Reject H₀ if t > 1.782

Quizplus · Accepted Answer

Since the sample sizes are both less than 30 and we do not know the population variances, we should use a t-test. At a significance level of .05 with a two-tailed test, the critical t-value with 21 degrees of freedom (the smaller of the two sample sizes minus 1) is 1.721. Therefore, we should reject the null hypothesis if the calculated t-value is greater than 1.721.

Given the Following Information About a Hypothesis Test of the Difference