A beer distributor claims that a new display featuring a life-size picture of a well-known rock singer will increase product sales in supermarkets by an average of 50 cases in a week. For a random sample of 20 high-volume liquor outlets, the average sales increase was 41.3 cases, and the sample standard deviation was 12.2 cases. Test at the 5% level the null hypothesis that the population mean sales increase is at least 50 cases, stating any assumptions you make.