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: 10; 6; 14; 3; 10; 10; 8; 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.
1.State the distribution to use for the test. (Enter your answer in the form
z
or
t
df
where
df
is the degrees of freedom.)
2.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= ?
3.What is the
p-value? (Round your answer to four decimal places.)
4.Indicate the correct decision ("reject" or "do not reject" the null hypothesis), the reason for it, and write an appropriate conclusion.
(i) Alpha (Enter an exact number as an integer, fraction, or decimal.)
? =
5. 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=
Upper=
Point estimate=