Two independent samples of sizes 20 and 25 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 45 degrees of freedom.
D) Student t distributed with 43 degrees of freedom.

Question

Quizplus · Accepted Answer

When testing the difference between two means from independent samples with equal variances, the test statistic follows a Student's t-distribution with degrees of freedom calculated using the formula: df = n1 + n2 - 2. Here, df = 20 + 25 - 2 = 43.

Two Independent Samples of Sizes 20 and 25 Are Randomly