Two independent samples of sizes 20 and 30 are randomly selected from two normally distributed populations.Assume that the population variances are unknown but equal.In order to test the difference between the population means, ,the sampling distribution of the sample mean difference, ,is:
A)normal.
B)Student-t with 50 degrees of freedom.
C)Student-t with 48 degrees of freedom.
D)None of these choices.

Question

Two independent samples of sizes 20 and 30 are randomly selected from two normally distributed populations.Assume that the population variances are unknown but equal.In order to test the difference between the population means,  ,the sampling distribution of the sample mean difference,  ,is:
A)normal. 
B)Student-t with 50 degrees of freedom. 
C)Student-t with 48 degrees of freedom. 
D)None of these choices.

Quizplus · Accepted Answer

The sampling distribution of the sample mean difference (also known as the sampling distribution of the difference between sample means) follows a Student-t distribution with degrees of freedom equal to the sum of the sample sizes minus two, which is 20+30-2=48. Therefore, the correct choice is C.

Two Independent Samples of Sizes 20 and 30 Are Randomly