Simulation. In this exercise, you are to perform a computer simulation to illustrate the sampling distribution of the difference between two sample means for independent samples, Key Fact 10.1 on page 466.

a. Simulate 1000 samples of size 12 from a normally distributed variable with a mean of 640 and a standard deviation of 70. Obtain the sample mean of each of the 1000 samples.

b. Simulate 1000 samples of size 15 from a normally distributed variable with a mean of 715 and a standard deviation of 150. Obtain the sample mean of each of the 1000 samples.

c. Obtain the difference, x¯1 − x¯2, for each of the 1000 pairs of sample means obtained in parts

(a) and (b).

d. Obtain the mean, the standard deviation, and a histogram of the 1000 differences found in part (c).

e. Theoretically, what are the mean, standard deviation, and distribution of all possible differences, x¯1 − x¯2?

f. Compare your answers from parts

(d) and (e).