A consumer product testing organization uses a survey of readersto obtain customer satisfaction ratings for the nation's largestsupermarkets. Each survey respondent is asked to rate a specifiedsupermarket based on a variety of factors such as: quality ofproducts, selection, value, checkout efficiency, service, and storelayout. An overall satisfaction score summarizes the rating foreach respondent with 100 meaning the respondent is completelysatisfied in terms of all factors. Suppose sample datarepresentative of independent samples of two supermarkets'customers are shown below.
| Supermarket 1 | Supermarket 2 |
|---|
n1 = 280 | n2 = 300 |
x1 = 89 | x2 = 88 |
(a)
Formulate the null and alternative hypotheses to test whetherthere is a difference between the population mean customersatisfaction scores for the two retailers. (Letμ1 = the population mean satisfaction score forSupermarket 1's customers, and let μ2 = thepopulation mean satisfaction score for Supermarket 2's customers.Enter != for ≠as needed.)
H0:
Ha:
(b)
Assume that experience with the satisfaction rating scaleindicates that a population standard deviation of 13 is areasonable assumption for both retailers. Conduct the hypothesistest.
Calculate the test statistic. (Use
μ1 − μ2.
Round your answer to two decimal places.)
Report the p-value. (Round your answer to four decimalplaces.)
p-value =
At a 0.05 level of significance what is your conclusion?
Reject H0. There is sufficient evidence toconclude that the population mean satisfaction scores differ forthe two retailers.Do not reject H0. There isnot sufficient evidence to conclude that the population meansatisfaction scores differ for the tworetailers.    Do not rejectH0. There is sufficient evidence to concludethat the population mean satisfaction scores differ for the tworetailers.Reject H0. There is not sufficientevidence to conclude that the population mean satisfaction scoresdiffer for the two retailers.
(c)
Which retailer, if either, appears to have the greater customersatisfaction?
Supermarket 1Supermarket 2Â Â Â Â neither
Provide a 95% confidence interval for the difference between thepopulation mean customer satisfaction scores for the two retailers.(Use
x1 − x2.
Round your answers to two decimal places.)
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