Problem

Independent random samples of 100 observations each are chosen from two normal populations...

Independent random samples of 100 observations each are chosen from two normal populations with the following means and standard deviations:

Population 1

Population 2

μ1 = 14

μ2 = 10

σ1 = 4

σ2 = 3

Let denote the two sample means.

a. Give the mean and standard deviation of the sampling distribution of
b. Give the mean and standard deviation of the sampling distribution of
c. Suppose you were to calculate the difference between the sample means. Find the mean and standard deviation of the sampling distribution of
d. Will the statistic be normally distributed? Explain