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;4;15;3;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.

A. State the null hypothesis.

H₀:10

H₀:<10

H_0: = 10

H₀: 10

B. State the alternative hypothesis.

H_a:= 10

H_a:10

H_a:10

H_a:>10

C. In words, state what your random variableXrepresents.

X represents the average number of sick days employees take each year.

X represents the average number of employees that call out sick for 10 days in one year.

X represents the number of sick days an employee takes in one year.

X represents the average number of employees that call out sick on a given day.

D. State the distribution to use for the test. (Enter your answer in the formzort_dfwheredfis the degrees of freedom.)

E. What is the test statistic? (If using thezdistribution round your answers to two decimal places, and if using thetdistribution round your answers to three decimal places.)

F. What is thep-value? (Round your answer to four decimal places.)

G. Explain what thep-value means for this problem.

IfH₀ is false, then there is a chance equal to thep-value that the average number of sick days for employees is at least as different from 10 as the mean of the sample is different from 10.

IfH₀ is true, then there is a chance equal to thep-value the average number of sick days for employees is not at least as different from 10 as the mean of the sample is different from 10.

IfH₀ is false, then there is a chance equal to thep-value the average number of sick days for employees is not at least as different from 10 as the mean of the sample is different from 10.

IfH_{0 i}s true, then there is a chance equal to thep-value that the average number of sick days for employees is at least as different from 10 as the mean of the sample is different from 10.

H. Sketch a picture of this situation. Label and scale the horizontal axis and shade the region(s) corresponding to thep-value.

I. Indicate the correct decision ("reject" or "do not reject" the null hypothesis), the reason for it, and appropriate conclusion.

(i) Alpha (Enter an exact number as an integer, fraction, or decimal.)

=

(ii) Decision:

reject the null hypothesis

do not reject the null hypothesis

(iii) Reason for decision:

Since<p-value, we do not reject the null hypothesis.

Since<p-value, we reject the null hypothesis.

Since>p-value, we do not reject the null hypothesis.

Since>p-value, we reject the null hypothesis.

iv) Conclusion:

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.

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.

(iv) Conclusion:

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.

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.