Many stock market observers say that when the P/E ratio for stocks gets over 20 the market is overvalued. The P/E ratio is the stock price divided by the most recent 12 months of earnings.

Suppose you are interested in seeing whether the current market is overvalued and would also like to know what proportion of companies pay dividends. A random sample of 30 companies listed on the New York Stock Exchange (NYSE) is provided (Barron’s, January 19, 2004).

Company Dividend P/E Ratio Company Dividend P/E Ratio Albertsons Yes 14 NY Times A Yes 25 BRE Prop Yes 18 Omnicare Yes 25 CityNtl Yes 16 PallCp Yes 23 DelMonte No 21 PubSvcEnt Yes 11 EnrgzHldg No 20 SensientTch Yes 11 Ford Motor Yes 22 SmtProp Yes 12 Gildan A No 12 TJX Cos Yes 21 HudsnUtdBcp Yes 13 Thomson Yes 30 IBM Yes 22 USB Hldg Yes 12 JeffPilot Yes 16 US Restr Yes 26 KingswayFin No 6 Varian Med No 41 Libbey Yes 13 Visx No 72 MasoniteIntl No 15 Waste Mgt No 23 Motorola Yes 68 Wiley A Yes 21 Ntl City Yes 10 Yum Brands No 18

a. What is a point estimate of the P/E ratio for the population of stocks listed on the New York Stock Exchange? Develop a 95% confidence interval.

b. Based on your answer to part (a), do you believe that the market is overvalued?

c. What is a point estimate of the proportion of companies on the NYSE that pay dividends? Is the sample size large enough to justify using the normal distribution to construct a confidence interval for this proportion? Why or why not?