10.75 Use a computer to demonstrate the truth of the statement describing the sampling distribution of x1  x2. Use two theoretical normal populations:

N1(100, 20) and N2(120, 20).

a. To get acquainted with the two theoretical populations, randomly select a very large sample from each. Generate 2000 data values, calculate mean and standard deviation, and construct a histogram using class boundaries that are multiples of one-half of a standard deviation

(10) starting at the mean for each population.

b. If samples of size eight are randomly selected from each population, what do you expect the distribution of x1  x2 to be like (shape of distribution, mean, standard error)?

c. Randomly draw a sample of size eight from each population, and find the mean of each sample. Find the difference between the sample means. Repeat 99 more times.

d. The set of 100 (x1  x2) values forms an empirical sampling distribution of x1  x2. Describe the empirical distribution: shape (histogram), mean, and standard error. (Use class boundaries that are multiples of standard error from mean for easy comparison to the expected.)

e. Using the information found in parts a–d, verify the statement about the x1  x2 sampling distribution made on page 564.

f. Repeat the experiment a few times and compare the results.

FYI See the Student Solutions Manual for additional information about commands.