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†.

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

(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.)

x =
s =

(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 for the P/E population mean ? of all large U.S. companies. (Round your answers to one decimal place.)

lower limit
upper limit

(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 is below average.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.

(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.

Answer 1

a)

xbar =25.2

s =15.5

b)

lower limit =21.6

upper limit=28.8

c)

for 99 % CI value of z=				2.576
margin of error E=z*std error                            =				5.59
lower confidence bound=sample mean-margin of error=				19.6
Upper confidence bound=sample mean +margin of error=				30.8

(please try lower bound =19.4 and upper limit =31.0 if above comes wrong)

d)

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

e) No ; According to the central limit theorem, when n ? 30, the x distribution is approximately normal.