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;15;5;11;10;7;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.)

• Part (a)
• What is the test statistic? (Round your answers to three decimal places.)
• t=______________
• Part (b) Multiple Choice

What is thep-value?

a) p-value < 0.010

b) 0.010 <p-value < 0.050

c) 0.050 <p-value < 0.100

d) p-value > 0.100

• Part (C)
• Construct a 95% confidence interval for the true mean.
• Sketch the graph of the situation.
• Label the point estimate and the lower and upper bounds of the confidence interval. (Round your answers to three decimal places.)
• Lower Bounds_____________ Point Estimate_______________ Upper Bounds________________