The mean number of sick days an employee takes per year is believed to be about ten. Members of a personnel department do not believe this figure. They randomly survey eight employees. The number of...

The mean number of sick days an employee takes per year is believed to be about ten. Members of a personnel department 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, and 13.

a) Find the mean and standard deviation of the sample.

b) Based on your sample, perform a test of hypothesis at the 10% level of significance to determine if the mean number of sick days of an employee is no longer 10 Use the critical value approach.