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, 3, 16, 4, 12, 8, 7, 7. Let $x$ = 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.
State the null and alternative hypotheses (in days). (Enter \mu for \mu as needed.)
$H_0$:
$H_a$:
What is the test statistic? (Round your answer to two decimal places.)
What is/are the critical value(s)? (If using the $z$ distribution round your answer(s) to two decimal places, and if using the $t$ distribution round your answer(s) to three decimal places. Enter \#N/A for any unused answer blanks.)
lower tail:
upper tail:
What is the decision of the test and what conclusions can be drawn?
$\circ$ At the 5% level of significance we would reject $H_0$ and conclude that there is sufficient evidence to conclude that the average number of sick days used per year by an employee is not equal to 10 days.
$\circ$ At the 5% level of significance we would fail to reject $H_0$ and conclude that there is sufficient evidence to conclude that the average number of sick days used per year by an employee is not equal to 10 days.
$\circ$ At the 5% level of significance we would reject $H_0$ and conclude that there is not sufficient evidence to conclude that the average number of sick days used per year by an employee is not equal to 10 days.
$\circ$ At the 5% level of significance we would fail to reject $H_0$ and conclude that there is not sufficient evidence to conclude that the average number of sick days used per year by an employee is not equal to 10 days.
