The price of a share of stock divided by the company\'s estimated future earning

Question

The price of a share of stock divided by the company's estimated future earnings per share is called the P/E ratio. High P/E ratios usually indicate "growth" stocks, or maybe stocks that are simply overpriced. Low P/E ratios indicate "value" 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 find the sample mean x and sample standard deviation s. (Round your answers to one decimal place.)

(b) Find a 90% confidence interval for the P/E population mean of all large U.S. companies. (Round your answers to one decimal place.)

(c) Find a 99% confidence interval for the P/E population mean of all large U.S. companies. (Round your answers to one decimal place.)

(d) Bank One (now merged with J. P. Morgan) 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?

We can say Bank One is below average, AT&T Wireless is above average, and Disney falls close to the average.We can say Bank One is below average, AT&T Wireless is above average, and Disney is above average.    We can say Bank One is above average, AT&T Wireless is below average, and Disney falls close to the average.We can say Bank One is below average, AT&T Wireless is above average, and Disney is below average.

(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? Hint: Use the central limit theorem.

Yes. According to the central limit theorem, when n 30, the x distribution is approximately normal.No. According to the central limit theorem, when n 30, the x distribution is approximately normal.   

11 35 19 13 15 21 40 18 60 72 9 20 29 53 16 26 21 14 21 27 10 12 47 14 33 14 18 17 20 19 13 25 23 27 5 16 8 49 44 20 27 8 19 12 31 67 51 26 19 18 32 The price of a share of stock divided by the company's estimated future earnings per share is called the P/E ratio. High P/E ratios usually indicate "growth" stocks, or maybe stocks that are simply overpriced. Low P/E ratios indicate "value" stocks or bargain stocks. A random sample of 51 of the largest companies in the United States gave the following P/E ratiost 11 35 19 13 15 21 40 18 60 72 9 20 29 53 16 26 21 14 21 27 10 12 47 14 33 14 18 17 20 1913 25 23 27 5 16 8 49 44 20 27 8 19 12 31 67 51 26 19 18 32 (a) Use a calculator with mean and sample standard deviation keys to find the sample mean x and sample standard deviation s. Round your answers to one decimal place.) (b) Find a 90% confidence interval for the P/E population mean of all large U.S. companies. (Round your answers to one decimal place.) lower lImit upper limit c) Find a 99% confidence interval or the P/E Population mean lower limit upper limit of all arge u. companies. Round your answers to one decimal place. (d Bank One now merged with·P. Morgan) had a P E o 12, AT T Wireless had a P/E of 72 and Disney had a PE of 24 Exam ne the confidence ntervais n parts b and would you describe these stocks at the time the sample was taken? How ·We can say Bank One is below average, AT&T; Wireless is above average, and Disney falls close to the average We can say Bank One is below average, AT&T; Wireless is above average, and Disney is above average. We can say Bank One is above average, AT&T; wireless is below average, and Disney falls close to the average we can say Bank One is below average, AT&T; Wireless is above average, and Disney is below average. (e) In previous problems, we assumed the x distrlbutlon was normal or approximately normal. Do we need to make such an assumption In this problem? Why or why not? Hint: Use the central limit theorem. Yes. According to the central limit theorem, when n No. According to the central limit theorem, when n 30, the x distribution is approximately normal. 30, the x distribution is approximately normal

Explanation / Answer

using ms-excel following information has been generated

(b) since n>30, we can use z-value for finding confidence interval

(1-alpha)*100% confidence interval for population mean=sample mean±z(alpha/2)*sd/sqrt(n)

90% confidence interval for population mean=sample mean±z(0.1/2)*sd/sqrt(n)=25.2±1.645*15.5/sqrt(51)

=25.2±3.6=(21.6, 28.8)

(c)99% confidence interval for population mean=sample mean±z(0.01/2)*sd/sqrt(n)=25.2±2.58*15.5/sqrt(51)

=25.2±5.6=(19.6, 30.8)

(d) We can say Bank One is below average (12<25.2), AT&T Wireless is above average (72>25.2), and Disney falls close to the average ( 24 and 25.2 is near by or close to each other)

(e) according to central limit theorem n>=30, the x distribution is approximately normal

n= 51 sum= 1284 mean=x= 25.2 s= 15.5

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