Question

A magazine uses a survey of readers to obtain customer satisfaction ratings for the nation's largest retailers. Each survey respondent is asked to rate a specified retailer in terms of six factors: quality of products, selection, value, checkout efficiency, service, and store layout. An overall satisfaction score summarizes the rating for each respondent with 100 meaning the respondent is completely satisfied in terms of all six factors. Sample data representative of independent samples of Retailer A and Retailer B customers are shown below.

Retailer A	Retailer B
n1 = 25	n2 = 30
x1 = 79	x2 = 71

(a)

Formulate the null and alternative hypotheses to test whether there is a difference between the population mean customer satisfaction scores for the two retailers. (Let μ₁ = population mean satisfaction score for Retailer A customers and μ₂ = population mean satisfaction score for Retailer B customers.)

H₀: μ₁ − μ₂ ≥ 0

H_a: μ₁ − μ₂ < 0

H₀: μ₁ − μ₂ ≠ 0

H_a: μ₁ − μ₂ = 0

    

H₀: μ₁ − μ₂ ≤ 0

H_a: μ₁ − μ₂ > 0

H₀: μ₁ − μ₂ = 0

H_a: μ₁ − μ₂ ≠ 0

H₀: μ₁ − μ₂ < 0

H_a: μ₁ − μ₂ = 0

(b)

Assume that experience with the satisfaction rating scale of the magazine indicates that a population standard deviation of 13 is a reasonable assumption for both retailers. Conduct the hypothesis test.

Find the value of the test statistic. (Round your answer to two decimal places.)

Find the p-value. (Round your answer to four decimal places.)

p-value =

At a 0.05 level of significance what is your conclusion?

Reject H₀. There is insufficient evidence to conclude that the population mean satisfaction scores differ for the two retailers.Reject H₀. There is sufficient evidence to conclude that the population mean satisfaction scores differ for the two retailers.    Do not Reject H₀. There is sufficient evidence to conclude that the population mean satisfaction scores differ for the two retailers.Do not reject H₀. There is insufficient evidence to conclude that the population mean satisfaction scores differ for the two retailers.

(c)

Provide a 95% confidence interval for the difference between the population mean customer satisfaction scores for the two retailers. (Round your answers to two decimal places.)

to

Which retailer, if either, appears to have the greater customer satisfaction?

The 95% confidence interval  ---Select--- is completely below contains is completely above zero. This suggests that the Retailer A has a  ---Select--- higher lower population mean customer satisfaction score than Retailer B.

Answer 1

Answer:

a)

Given,

n₁ = 25

n₂ = 30

x₁ = 79

x₂ = 71

s1 = s2 = 13

significance level = 0.05

Here we have to test

Null hypothesis

Ho : mu1 - mu2 = 0

Alternative hypothesis

H1 : mu1 - mu2 0

i.e.,

Option C is right answer.

b)

Now to test the test statistic

z = (x1 - x2)/sqrt(s1^2/n1 + s2^2/n2)

substitute the known values

= (79 - 71)/sqrt(13^2/25 + 13^2/30)

= 8/3.52042

z = 2.27

Now corresponding p value for the z = 2.27 is 0.0232

Here we can say that p value is less than significance level.

So that we reject the null hypothesis Ho.

Hence we can say that there is sufficient evidence to conclude that the population mean satisfaction scores differ for the two retailers.

c)

To determine the 95% confidence interval

For the 95%confidence interval, z value is 1.96

consider,

Interval = (x1 - x2) +/- z*sqrt(s1^2/n1 + s2^2/n2)

substitute the known values

= (79 - 71) +/- 1.96*sqrt(13^2/25 + 13^2/30)

= 8 +/- 1.96*3.52042

= 8 +/- 6.9000

= (8 - 6.9000 , 8 + 6.9000)

Interval = (1.1 , 14.9)

The 95% confidence interval is completely below contains is completely above zero.

This suggests that the Retailer A has a higher population mean customer satisfaction score than Retailer B.