7.15 Simulate taking midterms Assume that the distribution of the score on a recent midterm is bell shaped with population mean m = 70 and population standard deviation s = 10. You randomly sample n = 12 students who took the midterm. Using the Sampling Distribution of the Sample Mean web app accessible on the book’s website,

a. Simulate drawing one random sample of size 12. What sample mean score did you get? Why do you not expect to get exactly 70?

b. Now, simulate drawing 10,000 samples of size 12.

Describe the simulated sampling distribution by using the histogram of the 10,000 sample means you generated.

(Note: The app allows you to save the graph to a file.)

c. Suppose the population standard deviation is 5 rather than 10. Change to this setting in the app. How does the simulated sampling distribution of the sample mean change?