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 = 260	n2 = 300
x1 = 89	x2 = 88

(a) Formulate the null and alternative hypotheses to testwhether there 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:

H_a:

(b) Assume that experience with the satisfaction rating scaleindicates that a population standard deviation of 15 is areasonable assumption for both retailers. Conduct the hypothesistest.

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

test statistic =

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.

Reject H₀. There is not sufficient evidenceto conclude that the population mean satisfaction scores differ forthe two retailers.    

Do not reject H₀. There is not sufficientevidence to conclude that the population mean satisfaction scoresdiffer for the two retailers.

Do not reject H₀. There is sufficientevidence to conclude that the population mean satisfaction scoresdiffer for the two retailers.

(c) Which retailer, if either, appears to have the greatercustomer satisfaction?

Supermarket 1, Supermarket 2, or  neither

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