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, which of the following would best describe the test statistic?
A) It is a standard normal random variable.
B) It is an approximately standard normal random variable.
C) It is Student's t distributed with 58 degrees of freedom.
D) It is Student's t distributed with 33 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, which in this case is 25 + 35 - 2 = 58.

Two Independent Samples of Sizes 25 and 35 Are Randomly