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

Answer 1

The statistical software output for this problem is:

Summary statistics:

Column	Mean	Std. dev.
Data	25.176471	15.472176

One sample T confidence interval:
? : Mean of variable

90% confidence interval results:

Variable	Sample Mean	Std. Err.	DF	L. Limit	U. Limit
Data	25.176471	2.166538	50	21.545559	28.807383

99% confidence interval results:

Variable	Sample Mean	Std. Err.	DF	L. Limit	U. Limit
Data	25.176471	2.166538	50	19.37493	30.978011

Hence,

a) x = 25.2

s = 15.7

b) 90% confidence interval:

Lower limit = 21.5

Upper limit = 28.8

c) 99% confidence interval:

Lower limit = 19.4

Upper limit = 31.0