Question

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. F or Rite Aid, is the increase in the satisfaction score from year 1 to year 2 statistically significant? Use a = .05. What can you conclude?

b. C an you conclude that the year 2 score for Rite Aid is above the national average of 75.7? Use a = .05.

c. F or Expedia, is the increase from year 1 to year 2 statistically significant? Use a = .05.

d. When conducting a hypothesis test with the values given for the standard deviation, sample size, and a, how large must the increase from year 1 to year 2 be for it to be statistically significant? e. U se the result of part (d) to state whether the increase for J.C. Penney from year 1 to year 2 is statistically significant

Answer 1

Answer:

Given that

Company	Year 1	Year 2
Rite Aid	73	76
Expedia	75	77
J.C. Penney	77	78

n=60,

0 = 6pts

_a)

. F or Rite Aid, is the increase in the satisfaction score from year 1 to year 2 statistically significant? Use a = .05.

let null hypothesis

Ho: M1-M2= 0 D =0

H1: M1 - H2> 0 D > 0

Significance level:

g= 0,05

Standard error:

로

| +

$=\sqrt{\frac{36}{60}\times 2}$

जा

= 1.0954

(11 - 12) – (M1 – 12) S.E

(76 – 73) -(0) 1.0954

=37386

let upper tailed test

P - value = Plz > 2.7326) - 0.0031

we reject null hypothesis.

b)

An you conclude that the year 2 score for Rite Aid is above the national average of 75.7? Use a = .05.

Where null hypothesis;

Hp : 112 = 75.7

Alternate hypothesis:

H1 : M2 > 75.7

Significance level:

g= 0,05

u/

_76 – 75.7 6/V60

了=0.3873

let p-value = P(> 0.3873) = 0.3480

P - value is greater than significance level.

We fail to reject null hypothesis.

c)

F or Expedia, is the increase from year 1 to year 2 statistically significant? Use a = .05.

where null hypothesis:

HO: M1 – M2 = 0

H1:41 - M2 > 0

g= 0,05

(C) - C2)-(4-42) V+

(77-75)-(0) v +

= 1.8257

P - value = Plz > 1.8257)

= 0.0340.

P - value is less than significance level of

g= 0,05

So , we reject null hypothesis.

d)

When conducting a hypothesis test with the values given for the standard deviation, sample size, and a, how large must the increase from year 1 to year 2 be for it to be statistically significant.

Where Margin of error=

$Z_{0.05}\sqrt{\frac{\sigma ^{2}_{1}}{n_1}+\frac{\sigma _1^2}{n_2}}$

| = 1.6451 +-

= 1.80200

let increase is more than 1,8020 the increase is statistically significance.

e)

the result of part (d) to state whether the increase for J.C. Penney from year 1 to year 2 is statistically significant.

Let

01 - 12 = 78 – 77

$=1$

Let inverse is less than 1.8

finally the inverse is not statistically significant.