● Question 4#3A study was done to look at the relationship between number of vacation days employees take each yearand the number of sick days they take each year. The results of the survey are shown below.3Vacation Days 4 15 2 13 10 10Sick Days 31 90 1 4a. Find the correlation coefficient: r =b. The null and alternative hypotheses for correlation are:Ho: ?0H₁: ?0The p-value is:80O There is statistically significant evidence to conclude that an employee who takes morevacation days will take more sick days than an employee who takes fewer vacation days.O There is statistically insignificant evidence to conclude that there is a correlation between thenumber of vacation days taken and the number of sick days taken. Thus, the use of theregression line is not appropriate.O There is statistically significant evidence to conclude that there is a correlation between thenumber of vacation days taken and the number of sick days taken. Thus, the regression line isuseful.d. ² =e. Interpret 7²:O There is a 71% chance that the regression line will be a good predictor for the number of sickdays taken based on the number of vacation days taken.O There is statistically significant evidence to conclude that an employee who takes morevacation days will take fewer sick days than an employee who takes fewer vacation days.(Round to two decimal places)$14 50 84O There is a large variation in the number of sick days employees take, but if you only look atemployees who take a fixed number of vacation days, this variation on average is reduced by71%.F4Round to 2 decimal places.O Given any group with a fixed number of vacation days taken, 71% of all of those employees willtake the predicted number of sick days.071% of all employees will take the average number of sick days.%5F56F6MacBook Air&rF7*CDIIF8OF9 f. The equation of the linear regression line is:+=of sick days.(Please show your answers to two decimal places)g. Use the model to predict the number of sick days taken for an employee who took 2 vacation daysthis year.Sick Days =(Please round your answer to the nearest whole number.)h. Interpret the slope of the regression line in the context of the question:O The slope has no practical meaning since a negative number cannot occur with vacation daysand sick days.As x goes up, y goes down.O For every additional vacation day taken, employees tend to take on average 0.61 fewer sickdays.i. Interpret the y-intercept in the context of the question:O If an employee takes no vacation days, then that employee will take 9 sick days.The best prediction for an employee who doesn't take any vacation days is that the employeewill take 9 sick days.O The y-intercept has no practical meaning for this study.O The average number of sick days is predicted to be 9.

Question

● Question 4#3A study was done to look at the relationship between number of vacation days employees take each yearand the number of sick days they take each year. The results of the survey are shown below.3Vacation Days 4 15 2 13 10 10Sick Days 31 90 1 4a. Find the correlation coefficient: r =b. The null and alternative hypotheses for correlation are:Ho: ?0H₁: ?0The p-value is:80<F3(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 contextof the study.>O There is statistically significant evidence to conclude that an employee who takes morevacation days will take more sick days than an employee who takes fewer vacation days.O There is statistically insignificant evidence to conclude that there is a correlation between thenumber of vacation days taken and the number of sick days taken. Thus, the use of theregression line is not appropriate.O There is statistically significant evidence to conclude that there is a correlation between thenumber of vacation days taken and the number of sick days taken. Thus, the regression line isuseful.d. ² =e. Interpret 7²:O There is a 71% chance that the regression line will be a good predictor for the number of sickdays taken based on the number of vacation days taken.O There is statistically significant evidence to conclude that an employee who takes morevacation days will take fewer sick days than an employee who takes fewer vacation days.(Round to two decimal places)$14 50 84O There is a large variation in the number of sick days employees take, but if you only look atemployees who take a fixed number of vacation days, this variation on average is reduced by71%.F4Round to 2 decimal places.O Given any group with a fixed number of vacation days taken, 71% of all of those employees willtake the predicted number of sick days.071% of all employees will take the average number of sick days.%5F56F6MacBook Air&rF7*CDIIF8OF9 f. The equation of the linear regression line is:+=of sick days.(Please show your answers to two decimal places)g. Use the model to predict the number of sick days taken for an employee who took 2 vacation daysthis year.Sick Days =(Please round your answer to the nearest whole number.)h. Interpret the slope of the regression line in the context of the question:O The slope has no practical meaning since a negative number cannot occur with vacation daysand sick days.As x goes up, y goes down.O For every additional vacation day taken, employees tend to take on average 0.61 fewer sickdays.i. Interpret the y-intercept in the context of the question:O If an employee takes no vacation days, then that employee will take 9 sick days.The best prediction for an employee who doesn't take any vacation days is that the employeewill take 9 sick days.O The y-intercept has no practical meaning for this study.O The average number of sick days is predicted to be 9.

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