A study was done to look at the relationship between number of vacation days employees take each year and the number of sick days they take each year. The results of the survey are shown below. Vacation Days 3 13 16 12 | 1 13 15 Sick Days 4 0 10 10600 a. Find the correlation coefficient: r = b. The null and alternative hypotheses for correlation are: Ho:?v=0 H₁:? #0 The p-value is: Round to 2 decimal places. (Round to four decimal places) c. Use a level of significance of a = 0.05 to state the conclusion of the hypothesis test in the context of the study. There is statistically significant evidence to conclude that there is a correlation between the number of vacation days taken and the number of sick days taken. Thus, the regression line is useful. There is statistically significant evidence to conclude that an employee who takes more vacation days will take more sick days than an employee who takes fewer vacation days. There is statistically significant evidence to conclude that an employee who takes more vacation days will take fewer sick days than an employee who takes fewer vacation days O There is statistically insignificant evidence to conclude that there is a correlation between the number of vacation days taken and the number of sick days taken. Thus, the use of the regression line is not appropriate. a. The equation of the linear regression line is: ŷ- (Please show your answers to two decimal places) b. Use the model to predict the number of sick days taken for an employee who took 3 vacation days this year. Sick Days= (Please round to two decimal places.) c. Interpret the slope of the regression line in the context of the question: O As x goes up, y goes down. For every additional vacation day taken, employees tend to take on average 0.55 fewer sick days. The slope has no practical meaning since a negative number cannot occur with vacation days and sick days. d. Interpret the y-intercept in the context of the question: O The y-intercept has no practical meaning for this study. If an employee takes no vacation days, then that employee will take 7 sick days. The average number of sick days is predicted to be 7. The best prediction for an employee who doesn't take any vacation days is that the employee will take 7 sick days.