B. The attached data file has 500 rows and 20 columns. Treat each row as a sample of 20 observations, so you have 500 samples each of size 20. They were computer-generated, and I know that the population mean is 10 and the population variance is 2.5. If the usual form of the Central Limit Theorem applied here, the 500 sample means would follow, at least approximately, a N(10, 0.125) distribution. Show that this approximation is very poor for these data and find out which assumption or assumptions were violated.
C. A consequence of the result in B is that the "usual" t-distribution formula for a confidence interval for the population mean (8-50 on page 337 of the text) may not work very well with these data. Compute a 95% confidence interval using this formula for each of the 500 samples and count up how many of the intervals actually include the true value of the population mean. Does the formula give 95% coverage for these data? What can you conclude?
D. Do the following problems from Montgomery & Runger, Applied Statistics and Probability for Engineers, 2nd edition.
4-55, 4-56, 5-45, 5-80, 7-32, 7-34, 7-38, 8-33.