The mean number of sick days an employee takes per year is believed to be about 10. Members of a personnel department do not believe this figure. They randomly survey 8 employees. The number of sick days they took for the past year are as follows:11;5;13;4;10;8;8;8. LetX= the number of sick days they took for the past year. Should the personnel team believe that the mean number is about 10? Conduct a hypothesis test at the 5% level.

Note: If you are using a Student'st-distribution for the problem, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.)

1)What is the test statistic?

t=

2)What is thep-value? (Round your answer to four decimal places.)

3)Explain what thep-value means for this problem. Choose the correct anwser.

a) IfH₀ is false, then there is a chance equal to thep-value that the average number of sick days for employees is at least as different from 10 as the mean of the sample is different from 10

b)IfH₀ is true, then there is a chance equal to thep-value the average number of sick days for employees is not at least as different from 10 as the mean of the sample is different from 10.

c)IfH₀ is true, then there is a chance equal to thep-value that the average number of sick days for employees is at least as different from 10 as the mean of the sample is different from 10

d)IfH₀ is false, then there is a chance equal to thep-value the average number of sick days for employees is not at least as different from 10 as the mean of the sample is different from 10.