# BIA652 Homework – Statistical Inference Review – 04

September 13, 2019

BIA652 Homework – Statistical Inference Review – 04 (Please show all work, copy/paste as needed from any computer output) 1. 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 for 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. At a .05 level of significance what is your conclusion? c. Which retailer, if either, appears to have the greater customer satisfaction? Provide a 95% confidence interval for the difference between the population mean customer satisfaction scores for the two retailers. 2. Periodically, Merrill Lynch customers are asked to evaluate Merrill Lynch financial consultants and services. Higher ratings on the client satisfaction survey indicate better service, with 7 the maximum service rating. Independent samples of service ratings for two financial consultants are summarized here. Consultant A has 10 years of experience, whereas consultant B has 1 year of experience. Use α = .05 and test to see whether the consultant with more experience has the higher population mean service rating. a. State the null and alternative hypotheses. b. Compute the value of the test statistic. c. What is the p-value? d. What is your conclusion? 3. A manufacturer produces both a deluxe and a standard model of an automatic sander designed for home use. Selling prices obtained from a sample of retail outlets follow. a. The manufacturer’s suggested retail prices for the two models show a \$10 price differential. Use a .05 level of significance and test that the mean difference between the prices of the two models is \$10. b. What is the 95% confidence interval for the difference between the mean prices of the two models?

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