A magazine uses a survey of readers to obtain customersatisfaction ratings for the nation's largest retailers. Eachsurvey respondent is asked to rate a specified retailer in terms ofsix factors: quality of products, selection, value, checkoutefficiency, service, and store layout. An overall satisfactionscore summarizes the rating for each respondent with 100 meaningthe respondent is completely satisfied in terms of all six factors.Sample data representative of independent samples of Retailer A andRetailer 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 whetherthere is a difference between the population mean customersatisfaction scores for the two retailers. (Let?1 = population mean satisfaction score forRetailer A customers and ?2 = population meansatisfaction score for Retailer B customers.)
H0: ?1 ??2 ? 0
Ha: ?1 ??2 < 0
H0: ?1 ??2 ? 0
Ha: ?1 ??2 = 0
H0: ?1 ??2 ? 0
Ha: ?1 ??2 > 0
H0: ?1 ??2 = 0
Ha: ?1 ??2 ? 0
H0: ?1 ??2 < 0
Ha: ?1 ??2 = 0
(b)
Assume that experience with the satisfaction rating scale of themagazine indicates that a population standard deviation of 13 is areasonable assumption for both retailers. Conduct the hypothesistest.
Find the value of the test statistic. (Round your answer to twodecimal places.)
Find 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 insufficient evidence toconclude that the population mean satisfaction scores differ forthe two retailers.Reject H0. There issufficient 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.Do not reject H0. There isinsufficient evidence to conclude that the population meansatisfaction scores differ for the two retailers.
(c)
Provide a 95% confidence interval for the difference between thepopulation 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 customersatisfaction?
The 95% confidence interval ---Select--- iscompletely below contains is completely above zero. This suggeststhat the Retailer A has a ---Select--- higher lowerpopulation mean customer satisfaction score than Retailer B.
