Two independent samples of sizes 25 and 35 are randomly selected from two normal populations with equal variances. 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
E) Student t-distributed with 18 degrees of freedom

Question

Quizplus · Accepted Answer

When comparing means from two independent samples (with equal variances) from normal populations, the test statistic follows a Student's t-distribution. The degrees of freedom (df) for this test are calculated using the formula df = n1 + n2 - 2, where n1 and n2 are the sample sizes. Here, df = 25 + 35 - 2 = 58.

Two Independent Samples of Sizes 25 and 35 Are Randomly