Consumer Reports uses a survey of readers to obtain customer satisfaction ratings for the nation's largest retailers (Consumer Reports, March 2012). 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 Target and Walmart customers are shown below.
a. Formulate the null and alternative hypotheses to test whether there is a difference between the population mean customer satisfaction scores the two retailers.
b. Assume that experience with the Consumer Reports satisfaction rating scale indicates that a population standard deviation of 12 is a reasonable assumption for both retailers. Conduct the hypothesis test and report the p-value. Round your answer to four decimal places.
At a .05 level of significance what is your conclusion?
c. Provide a 95% confidence interval for the difference between the population mean customer satisfaction scores for the two retailers. Which retailer, if either, appears to have the greater customer satisfaction?