In a Good Housekeeping article, the organization reports that while washing machines have become more efficient in the last several years, washing machine manufacturers are finding it difficult to satisfy recently updated federal energy rules without sacrificing cleaning (Good Housekeeping website, January 20, 2013). Is there a difference in how clean front-loading washing machines and top-loading washing machines will get a load of laundry? A sample of 42 owners of top-loading washing machines and 49 front-loading washing machines purchased in 2012 were asked to rate their washing machines on how well they cleaned laundry. All washing machines are rated on a 100-point scale, with higher values indicating cleaner laundry. Ratings given by owners of top-loading machines had an average rating of 82.55, and the owners of front-loading machines provided an average rating of 77.46. Assume that the population standard deviation is 6.18 for ratings of top-loading machines and 5.97 for ratings of front-loading machines.

a. What is the point estimate of the difference between the population mean rating for top-loading washing machines and front-loading washing machines?

b. At 95% confidence, what is the margin of error?

c. What is a 95% confidence interval estimate of the difference between the population mean ratings for the two types of washing machines?