A securities analyst wants to estimate the average percentage of institutional holding of all publicly traded stocks in the United States. The analyst believes that stocks traded on the three major exchanges have different characteristics and therefore decides to use stratified random sampling. The three strata are the New York Stock Exchange (NYSE), the American Exchange (AMEX), and the Over the Counter (OTC) exchange. The weights of the three strata, as measured by the number of stocks listed in each exchange, divided by the total number of stocks, are NYSE, 0.44; AMEX, 0.15; OTC, 0.41. A total random sample of 200 stocks is selected, with proportional allocation. The average percentage of institutional holdings of the subsample selected from the issues of the NYSE is 46%, and the standard deviation is 8%.
The corresponding results for the AMEX are 9% average institutional holdings and a standard deviation of 4%, and the corresponding results for the OTC stocks are 29% average institutional holdings and a standard deviation of 16%.
a. Give a stratified estimate of the mean percentage of institutional holdings per stock.
b. Give the standard error of the estimate in a.
c. Give a 95% confidence interval for the mean percentage of institutional holdings.