A study was done to look at the relationship between number ofvacation days employees take each year and the number of sick daysthey take each year. The results of the survey are shown below.

Vacation Days	2	15	4	5	2	0	3	3	11
Sick Days	4	0	4	5	6	10	5	3	0

1. Find the correlation coefficient: r=r=   Roundto 2 decimal places.
2. The null and alternative hypotheses for correlation are:
   H0:H0: ? r ρ μ  == 0
   H1:H1: ? r ρ μ   ≠≠ 0
   The p-value is:    (Round to four decimalplaces)
   
3. Use a level of significance of α=0.05α=0.05 to state theconclusion of the hypothesis test in the context of the study.
   • There is statistically significant evidence to conclude thatthere is a correlation between the number of vacation days takenand the number of sick days taken. Thus, the regression line isuseful.
   • There is statistically insignificant evidence to conclude thatthere is a correlation between the number of vacation days takenand the number of sick days taken. Thus, the use of the regressionline is not appropriate.
   • There is statistically significant evidence to conclude that anemployee who takes more vacation days will take more sick days thanan employee who takes fewer vacation days.
   • There is statistically significant evidence to conclude that anemployee who takes more vacation days will take fewer sick daysthan an employee who takes fewer vacation days .
4. r2r2 =  (Round to two decimal places)
5. Interpret r2r2 :
   • Given any group with a fixed number of vacation days taken, 71%of all of those employees will take the predicted number of sickdays.
   • 71% of all employees will take the average number of sickdays.
   • There is a large variation in the number of sick days employeestake, but if you only look at employees who take a fixed number ofvacation days, this variation on average is reduced by 71%.
   • There is a 71% chance that the regression line will be a goodpredictor for the number of sick days taken based on the number ofvacation days taken.
6. The equation of the linear regression line is:  
   ˆyy^ =  + xx   (Please show your answersto two decimal places)
   
7. Use the model to predict the number of sick days taken for anemployee who took 2 vacation days this year.
   Sick Days =  (Please round your answer to the nearestwhole number.)
   
8. Interpret the slope of the regression line in the context ofthe question:
   • As x goes up, y goes down.
   • For every additional vacation day taken, employees tend to takeon average 0.53 fewer sick days.
   • The slope has no practical meaning since a negative numbercannot occur with vacation days and sick days.
9. Interpret the y-intercept in the context of the question:
   • If an employee takes no vacation days, then that employee willtake 7 sick days.
   • The best prediction for an employee who doesn't take anyvacation days is that the employee will take 7 sick days.
   • The y-intercept has no practical meaning for this study.
   • The average number of sick days is predicted to be 7.