Two independent samples of sizes 25 and 35 are randomly selected from two normal populations with equal variances (assumed to be unknown).In order to test the difference between the population means,the test statistic is:
A)a standard normal random variable.
B)approximately standard normal random variable.
C)Student t-distributed with 58 degrees of freedom.
D)Student t-distributed with 33 degrees of freedom.

Question

Quizplus · Accepted Answer

When the population variances are unknown, we use the t-distribution to test the difference between population means. Since the sample sizes are different, we use the pooled variance and the degrees of freedom are (n1-1) + (n2-1) = 58. Therefore, the correct choice is C, Student t-distributed with 58 degrees of freedom.

Two Independent Samples of Sizes 25 and 35 Are Randomly