Two independent samples of sizes 50 and 50 are randomly selected from two populations to test the difference between the population means, .The sampling distribution of the sample mean difference is:
A)normally distributed
B)approximately normal
C)t - distributed with 98 degrees of freedom
D)chi-squared distributed with 99 degrees of freedom

Question

Two independent samples of sizes 50 and 50 are randomly selected from two populations to test the difference between the population means,  .The sampling distribution of the sample mean difference  is:
A)normally distributed 
B)approximately normal 
C)t - distributed with 98 degrees of freedom 
D)chi-squared distributed with 99 degrees of freedom

Quizplus · Accepted Answer

The sampling distribution of the sample mean difference is approximately normal due to the central limit theorem, which states that the sampling distribution of the sample mean is approximately normal for large sample sizes (n > 30) regardless of the distribution of the population. Since both samples have n = 50, the sampling distribution of the sample mean difference is approximately normal.

Two Independent Samples of Sizes 50 and 50 Are Randomly