A study was done and the number y i shown below 0 6 2 5 Find the carr EDefficient: r 0.709 Round to 2 decimal places 3. The null and alternative hypothe is for correlation are: The p-value is D.02 181 (Round to four decimal places) . 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 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. 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 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. [Round to two decimal places) e. Interpret r : O 68x of all employees will take the average number of sick days. O Given any group with a fixed number of vacation days taken, 68% of all of those employees will take the predicted number of sick days. 3 There is a large variation in the number of sick days employees take, but if you only look at employees who take a fixed number of vacation days, this variation on average is reduced by There is a 68% chance that the regression line will be a good predictor for the number of sick day's taken based on the number of vacation days taken. 1. The equation of the Linear regression line is: (Please show your answers to two decimal places) 1. Use the model to predict the number of sick days taken for an employee who took 2 vacation days this year. Sick Days Please round your answer to the nearest whole number.) he Interpret the slope of the regression line in the context of the question: IFor every additional vacation day taken, employees tend to take on average 0. 44 fewer sick As x goes up. y goes down The close has no practical meaning since a negative number cannot occur with vacation days and sick days. Interpret the y intercept in the context of the questions The best prediction for an employee -he doesnt take any vacation days is that the employee will take " sick days. Ill an employee takes no vacation offs, then that amaipage will take s sick days the y intercept has no practical meaning for this study average number Hint: Helpful ides on the Linear Regression 9Question 10 The following table shows retail sales in drug stores in billions of dollars in the U.S. for years since 199 Year Retail Sales 0 85.851 3 108.426 6 141.781 9 169.256 12 202.297 15 222.266 Let S(t) be the retails sales in billions of dollars in t years since 1995. A linear model for the data is F(t) = 9.44t + 84.182. 220 210 200 190 180 170- 160 150 140 130 120 100- 90 12 15 80 Use the above scatter plot to decide whether the linear model fits the data well. The function is a good model for the data. The function is not a good model for the data Estimate the retails sales in the U. S. in 2017. billions of dollars. Use the model to predict the year that corresponds to retails sales of $230 billion.Question 11 You wish to determine if there is a positive linear correlation between the age of a driver and the number of driver deaths. The following table represents the age of a driver and the number of driver deaths per 100,000. Use a significance level of 0.05 and round all values to 4 decimal places. Driver Age Number of Driver Deaths per 100,000 29 20 42 20 61 22 52 32 67 29 61 31 29 19 32 21 53 23 70 27 Ho: p = 0 Ha: p > 0 Find the Linear Correlation Coefficient Find the p-value p-value = The p-value is Less than (or equal to) a O Greater than a The p-value leads to a decision to Accept Ho Reject Ho Do Not Reject Ho The conclusion is There is a significant linear correlation between driver age and number of driver deaths. There is insufficient evidence to make a conclusion about the linear correlation between driver age and number of driver deaths. There is a significant negative linear correlation between driver age and number of driver deaths. There is a significant positive linear correlation between driver age and number of driver deaths. .em_Id=74932693 . Question 12 What is the relationship between the attendance at a major league ball game and the total number of runs below. scored? Attendance figures (in thousands) and the runs scored for 11 randomly selected games are shown Attendance 17 41 34 26 32 17 50 17 45 15 59 Runs 1 6 4 5 7 6 6 8 1 7 a. Find the correlation coefficient: r = Round to 2 decimal places. b. The null and alternative hypotheses for correlation are: Ho: 7v = 0 The p-value is: (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 O There is statistically significant evidence to conclude that a game with a higher attendance will have more runs scored than a game with lower attendance. O There is statistically significant evidence to conclude that there is a correlation between the attendance of baseball games and the runs scored. Thus, the regression line is useful. O There is statistically insignificant evidence to conclude that there is a correlation between the attendance of baseball games and the runs scored. Thus, the use of the regression line is not appropriate. There is statistically significant evidence to conclude that a game with higher attendance will have fewer runs scored than a game with lower attendance. d. 72 (Round to two decimal places) (Round to two decimal places) e. Interpret r )Given any fixed attendance, 38% of all of those games will have the predicted number of runs scored. There is a large variation in the runs scored in baseball games, but if you only look at games with a fixed attendance, this variation on average is reduced by 38%. 38% of all games will have the average number of runs scored. There is a 38% chance that the regression line will be a good predictor for the runs scored based on the attendance of the game. f. The equation of the linear regression line is: (Please show your answers to two decimal places) g. Use the model to predict the runs scored at a game that has an attendance of 37,000 people. Runs scored - (Please round your answer to the nearest whole number. ) h. Interpret the slope of the regression line in the context of the question: As x goes up, y goes up. For every additional thousand people who attend a game, there tends to be an average increase of 0.09 runs scored. The slope has no practical meaning since the total number runs scored in a game must be positive. . Interpret the y-intercept in the context of the question if the attendance of a baseball game is 0, then 2 runs will be scored. The y-intercept has no practical meaning for this study. The best prediction for a game with 0 attendance is that there will be 2 runs scored. The average runs scored is predicted to be 2