The price of a share of stock divided by a company€™s estimated future earnings per share is called the P/E ratio. High P/E ratios usually indicate €œgrowth€ stocks, or maybe stocks that are simply overpriced. Low P/E ratios indicate €œvalue€™€™ stocks or bargain stocks. A random sample of 51 of the largest companies in the United States gave the following P/E ratios:

(a) Use a calculator with mean and sample standard deviation keys to verify that ‰ˆ 25.2 and s ‰ˆ 15.5.
(b) Find a 90% confidence interval for the P/E population mean μ of all large U.S. companies.
(c) Find a 99% confidence interval for the P/E population mean μ of all large U.S. companies.
(d) Bank One (now merged with JP Morgan Chase) had a P/E of 12, AT&T Wireless had a P/E of 72, and Disney had a P/E of 24. Examine the confidence intervals in parts (b) and (c). How would you describe these stocks at the time the sample was taken?
(e) In previous problems, we assumed the x distribution was normal or approximately normal. Do we need to make such an assumption in this problem? Why or why not?

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