The mean number of sick days an employee takes per year is believed to be about 10. Members of a personnel department do

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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; 5; 11; 9; 7; 10.
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.)
State the distribution to use for the test. (Enter your answer
in the
form z or tdf where df is
the degrees of freedom.)
What is the p value?
p=
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.)
t=
What is the alpha?
a=
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.)