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 μ 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 μ of all large U.S. companies. (Round your answers to one decimal place.)

lower limit
upper limit

Answer 1

a. For the given data

And sample standard deviation is calculated as below

Create the following table.

data	data-mean	(data - mean)2
11	-14.1765	200.97315225
35	9.8235	96.50115225
19	-6.1765	38.14915225
13	-12.1765	148.26715225
15	-10.1765	103.56115225
21	-4.1765	17.44315225
40	14.8235	219.73615225
18	-7.1765	51.50215225
60	34.8235	1212.67615225
72	46.8235	2192.44015225
9	-16.1765	261.67915225
20	-5.1765	26.79615225
29	3.8235	14.61915225
53	27.8235	774.14715225
16	-9.1765	84.20815225
26	0.8235	0.67815225
21	-4.1765	17.44315225
14	-11.1765	124.91415225
21	-4.1765	17.44315225
27	1.8235	3.32515225
10	-15.1765	230.32615225
12	-13.1765	173.62015225
47	21.8235	476.26515225
14	-11.1765	124.91415225
33	7.8235	61.20715225
14	-11.1765	124.91415225
18	-7.1765	51.50215225
17	-8.1765	66.85515225
20	-5.1765	26.79615225
19	-6.1765	38.14915225
13	-12.1765	148.26715225
25	-0.1765	0.03115225
23	-2.1765	4.73715225
27	1.8235	3.32515225
5	-20.1765	407.09115225
16	-9.1765	84.20815225
8	-17.1765	295.03215225
49	23.8235	567.55915225
44	18.8235	354.32415225
20	-5.1765	26.79615225
27	1.8235	3.32515225
8	-17.1765	295.03215225
19	-6.1765	38.14915225
12	-13.1765	173.62015225
31	5.8235	33.91315225
67	41.8235	1749.20515225
51	25.8235	666.85315225
26	0.8235	0.67815225
19	-6.1765	38.14915225
18	-7.1765	51.50215225

Find the sum of numbers in the last column to get.

So

b. Now as sample size is greater than 30, we will use z distribution to find CI

z value for 90% CI is 1.645 as P(-1.645<z<1.645)=0.90

So Margin of Error is

Hence CI is

Lower limit is 21.6

Upper limit is 28.8

c. For 99% CI z value is 2.58 as P(-2.58<z<2.58)=0.99

So Margin of Error is

Hence CI is

Lower limit is 19.6

Upper limit is 30.8