The Money & Investing section of The Wall Street Journal contains a summary of daily investment performance for stock exchanges, overseas markets, options, commodities, futures, and so on. In the New York Stock Exchange section, information is provided on each stock's 52 week high price per share, 52 week low price per share, dividend rate, yield, P/E ratio, daily volume, daily high price per share, daily low price per share, closing price per share, and daily net change. The P/E(price/earning) ratio for each stock is determined by dividing the price of a share of stock by the earnings per share reported by the company for the most recent four quarters. A sample of 10 stocks taken from The Wall Street Journal (September 29, 2000) provided the following data on P/E ratios: 5, 7, 9, 10, 14, 23, 20, 15, 3, 26.
a. What is the point estimate of the mean P/E ratio for the population of all stocks listed on the New York Stock Exchange?
b. What is the point estimate of the standard deviation of the P/E ratios for the population of all stocks listed on the NYSE?
c. At 95% confidence, what is the interval estimate of the mean P/E ratio for the population of all stocks listed on the NYSE? Assume that the population has a normal distribution.
d.Comment on the precision of the results.
7. In the previous problem, test to determine if the true mean P/E ratio is greater than 12.
8. In #7, state what decisions would constitute Type I and Type II errors.