Independent random samples of 64 observations each are chosen from two normal populations with the following means and standard deviations:
Population 1 Population 2
µ1 = 12 µ2 = 10
?1 = 4 ?2 = 3
Let x-bar1 and x-bar2 denote the two sample means.
a. Give the mean and standard deviation of the sampling distribution of x-bar 1 .
b. Give the mean and standard deviation of the sampling distribution of x-bar2 .
c. Suppose you were to calculate the difference (x-bar1 - x-bar2) between the sample means. Find the mean and standard deviation of the sampling distribution of (x-bar1 - x-bar2).
d. Will the statistic (x-bar1 - x-bar2) be normally distributed? Explain.