A market research firm supplies manufactures with estimates of the retail sales of their products from samles of retail stores. Marketing managers are prone to look at the estimates and ignore sampling error. An SRS of 75 stores this month shows mean sales of 52 units of a small appliance, with standard deviation 13 units. During the same month last year, an SRS of 53 stores gave mean sales of 49 units, with standard deviation of 11 units. An increase from 49 to 52 is a rise of 6%. The marketing manager is happy because sales went up 6%.
Should the manager be happy about this improvement? Explain using a significance test.
Find a 95% confidence interval for the difference between this year and last year in the mean number of units sold at all retail stores and interpret the results.