This is an exercise using Excel. (a) Use =RANDBETWEEN(0,99) to create 20 samples of size n = 4 by choosing two digit random numbers between 00 and 99 (see illustration below). (b) For each sample, calculate the mean. (c) Make a histogram of the 80 individual X values using bins 10 units wide (i.e., 0, 10, 20, . . . , 100). Describe the shape of the histogram. (d) Make a histogram of your 20 sample means using bins 10 units wide. (e) Discuss the histogram shape. Does the Central Limit Theorem seem to be working? (f) Find the mean of the sample means. Was it what you would expect by the CLT? Explain. (g) Find the average standard deviation of the sample means. Was it what you would expect by the CLT? (h) What was the point of this exercise?

Biting an unpopped kernel of popcorn hurts! As an experiment, a self confessed connoisseur of cheap popcorn carefully counted 773 kernels and put them in a popper. After popping, the unpopped kernels were counted. There were 86.

(a) Construct a 90 percent confidence interval for the proportion of all kernels that would not pop. (b) Check the normality assumption. (c) Try the Very QuickRule. Does it work well here? Why, or why not? (d) Why might this sample not be typical?