Two independent samples of sizes 40 and 50 are randomly selected from two populations to test the difference between the population means . Which of the following best describes the sampling distribution of the sample mean difference ?
A) It is normally distributed.
B) It is approximately normal.
C) It is Student's t distributed, with 88 degrees of freedom.
D) It is t distributed, with 88 degrees of freedom.

Question

Two independent samples of sizes 40 and 50 are randomly selected from two populations to test the difference between the population means  . Which of the following best describes the sampling distribution of the sample mean difference  ?
A) It is normally distributed. 
B) It is approximately normal. 
C) It is Student's t distributed, with 88 degrees of freedom. 
D) It is t distributed, with 88 degrees of freedom.

Quizplus · Accepted Answer

The sampling distribution of the sample mean difference is approximately normal because both sample sizes are greater than 30. When sample sizes are sufficiently large, the central limit theorem states that the sampling distribution of the sample mean difference will be approximately normal regardless of the shape of the underlying population distributions. Therefore, options C and D (which both suggest a Student's t distribution) are not appropriate here as they assume smaller sample sizes and/or unknown population standard deviations.

Two Independent Samples of Sizes 40 and 50 Are Randomly