In: Statistics and Probability
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; 6; 13;
5; 9; 9; 6; 8. 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.
Note: If you are using a Student's t-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? (If using the z distribution round your answers to two decimal places, and if using the t distribution round your answers to three decimal places.)
2. What is the p-value? (Round your answer to four decimal places.)
3. 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.)