A health club manager claims that members lose an average of 15 pounds during the first six months of membership. A sample of fifteen members of the club showed they lost an average of 11.5 pounds during the first six months of membership with a standard deviation of 2.2 pounds. Test at the 5% significance level if the mean weight loss during the first six months of their membership by all members of this health club is less than 15 pounds

and

A computer company that recently introduced a new software product claims that the mean time it takes to learn this new software product is not more than 2 hours for people who are somewhat familiar with computers. A random sample of twelve such persons was selected. The following data give the time taken in hours by these persons to learn to use the software.

1.75 2.25 2.40 1.90 1.50 2.75

2.15 2.25 1.80 2.20 3.25 2.60

Test at the 1% significance level whether the company’s claim is true. Assume that the times taken by all persons who are somewhat familiar with computers to learn how to use this software are approximately normally distributed.

thanks in advance!