Question

You may need to use the appropriate appendix table or technology to answer this 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 = 80	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 12 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 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.      Reject H₀. There is insufficient 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 above contains is completely below zero. This suggests that the Retailer A has a  ---Select--- higher lower population mean customer satisfaction score than Retailer B.

Answer 1

Given: h 2s- ne-30 X2-ニチ) 02-12 X1 80 に12 Cb) Test statistic X1X2 2 612 80-刊 2 n) 30 C12) 9 3.2496 Reject Ho There is sufficient evidence to condude that the population meao scatistaction scores differ for the ttoo retailers ce) g5% confidence interval is ni

(l2 from 2-table 30 9 t 2692 The g5% confidence interval is (4463 -15-33) The gs nterval 1s zexo Tis suggest that the Retailer A has higher above bopulation mean customes gatistaction Score than e tciler B