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Will improving customer service result in higher stock prices for the companies providing the better service? “When a company’s satisfaction score has improved over the prior year’s results and is above the national average (75.7), studies show its shares have a good chance of outperforming the broad stock market in the long run.” The following satisfaction scores of three companies for the 4th quarters of two previous years were obtained from the American Customer Satisfaction Index. Assume that the scores are based on a poll of 60 customers from each company. Because the polling has been done for several years, the standard deviation can be assumed to equal 6 points in each case. Company Year 1 Year 2 Rite Aid 73 76 Expedia 75 77 J.C. Penney 77 78 a. For Rite Aid, is the increase in the satisfaction score from year 1 to year 2 statistically significant? Use α = .05. What can you conclude? b. Can you conclude that the year 2 score for Rite Aid is above the national average of 75.7? Use α = .05. c. For Expedia, is the increase from year 1 to year 2 statistically significant? Use α = .05. d. When conducting a hypothesis test with the values given for the standard deviation, sample size, and α , how large must the increase from year 1 to year 2 be for it to be statistically significant? e. Use the result of part (d) to state whether the increase for J.C. Penney from year 1 to year 2 is statistically significant.

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STATISTICS F/BUSINESS+ECONOMICS-TE...

13th Edition
Anderson
Publisher: CENGAGE L
ISBN: 9781305881884

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STATISTICS F/BUSINESS+ECONOMICS-TE...

13th Edition
Anderson
Publisher: CENGAGE L
ISBN: 9781305881884
Chapter 10.1, Problem 8E
Textbook Problem
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Will improving customer service result in higher stock prices for the companies providing the better service? “When a company’s satisfaction score has improved over the prior year’s results and is above the national average (75.7), studies show its shares have a good chance of outperforming the broad stock market in the long run.” The following satisfaction scores of three companies for the 4th quarters of two previous years were obtained from the American Customer Satisfaction Index. Assume that the scores are based on a poll of 60 customers from each company. Because the polling has been done for several years, the standard deviation can be assumed to equal 6 points in each case.

Company Year 1 Year 2
Rite Aid 73 76
Expedia 75 77
J.C. Penney 77 78
  1. a. For Rite Aid, is the increase in the satisfaction score from year 1 to year 2 statistically significant? Use α = .05. What can you conclude?
  2. b. Can you conclude that the year 2 score for Rite Aid is above the national average of 75.7? Use α = .05.
  3. c. For Expedia, is the increase from year 1 to year 2 statistically significant? Use α = .05.
  4. d. When conducting a hypothesis test with the values given for the standard deviation, sample size, and α, how large must the increase from year 1 to year 2 be for it to be statistically significant?
  5. e. Use the result of part (d) to state whether the increase for J.C. Penney from year 1 to year 2 is statistically significant.

a.

To determine

Test whether it can be concluded that the increase in the satisfaction score from year-1 to year-2 is statistically significant or not at α=.05.

Explanation of Solution

Calculation:

The satisfaction scores of three companies for the 4th quarters of two previous years which are obtained from the American Customer Satisfaction Index are as follows,

CompanyYear 1Year 2
Rite Aid7376
Expedia7577
J.C.Penney7778

Consider the scores are based on a poll of 60 customers from each company and the standard deviation equals to 6 points in each case. The national average is 75.7.

Here μ1 represents the population mean satisfaction score of Rite Aid in year 2 and μ2 represents the population mean satisfaction score of Rite Aid in year 1.

State the hypothesis:

The test hypotheses are as follows:

Null hypothesis:

H0:μ1μ20

That is, there is no increasein the satisfaction scores of Rite Aid form year 1 to year 2.

Alternative hypothesis:

Ha:μ1μ2>0

That is, there is an increase in the satisfaction scores of Rite Aid form year 1 to year 2.

Test statistic:

The test statistic for hypothesis test of μ1μ2 when σ1 and σ2 are known is,

z=(x¯1x¯2)D0σ12n1+σ22n2

Substitute x¯1 as 76, x¯2 as 73, σ1</

b.

To determine

Test whether it can be concluded that the year-2 score for Rite Aid is above the national average of 75.7 or not at α=.05.

c.

To determine

Check whether it can be concluded that the increase from year-1 to year-2 for Expedia is statistically significant or not at α=.05.

d.

To determine

Find the increase in J.C Penney that makes the results from year 1 to year 2 to be statistically significant

e.

To determine

Check whether the increase for J.C. Penney from year 1 to year 2 is statistically significantor not.

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Chapter 10 Solutions

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