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
σ1 = 4 ................................. σ2 = 3
Let x̅1 and x̅2 denote the two sample means.
a. Give the mean and standard deviation of the sampling distribution of x̅1.
b. Give the mean and standard deviation of the sampling distribution of x̅2.
c. Suppose you were to calculate the difference between the sample means (x̅1 - x̅2). Find the mean and standard deviation of the sampling distribution of (x̅1 - x̅2).
d. Will the statistic (x̅1 - x̅2) be normally distributed? Explain.