A consumer product testing organization uses a survey of readers to obtain customer satisfaction ratings for the nation's largest supermarkets. Each survey respondent is asked to rate a specified...


A consumer product testing organization uses a survey of readers to obtain customer satisfaction ratings for the nation's largest supermarkets. Each survey respondent is asked to rate a specified supermarket based on a variety of factors such as: 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 factors. Suppose sample data representative of independent samples of two supermarkets' customers are shown below.
















Supermarket 1Supermarket 2

n1 = 290


n2 = 300


x1 = 89


x2 = 88



(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 = the population mean satisfaction score for Supermarket 1's customers, and let μ2 = the population mean satisfaction score for Supermarket 2's customers. Enter != for ≠ as needed.)



H
0:




H
a:








(b)


Assume that experience with the satisfaction rating scale indicates that a population standard deviation of 16 is a reasonable assumption for both retailers. Conduct the hypothesis test.

Calculate the test statistic. (Use μ1 − μ2. Round your answer to two decimal places.)

(         )

Report thep-value. (Round your answer to four decimal places.)


p-value = (       )


At a 0.05 level of significance what is your conclusion?


RejectH
0. There is not sufficient evidence to conclude that the population mean satisfaction scores differ for the two retailers.

RejectH
0. There is sufficient evidence to conclude that the population mean satisfaction scores differ for the two retailers.

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

Do not rejectH
0. There is not sufficient evidence to conclude that the population mean satisfaction scores differ for the two retailers.






(c)


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



Supermarket 1

Supermarket 2

neither



Provide a 95% confidence interval for the difference between the population mean customer satisfaction scores for the two retailers. (Use
x1 − x2. Round your answers to two decimal places.)


(        to         )


Jun 03, 2022
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