Suppose that a committee is studying whether there is waste of time in our judicial system or not. It is interested in the mean amount of time individuals waste at the courthouse waiting to be called for jury duty. The committee surveyed 81 recent jurors at random. The sample mean wait time was eight hours with a sample standard deviation of four hours. Construct and interpret a 95% confidence interval for the population mean time wasted.

Assume that the mean number of sick days an employee takes per year is normally distributed with a mean of ten days. Members of a personnel team do not believe this figure. They randomly survey eight employees. The number of sick days they took for the past year are as follows: 12; 4; 15; 3; 11; 8; 6; 8. Test the hypothesis that the mean number of sick days an employee takes per year differs from ten days with = 0.10.