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. Question 8 0/5 pts 0 3 # 99 0 Det What is the relationship between the amount of time statistics students study per week and their final exam scores? The results of the survey are shown below. Time 5 4 2 1 8 0 14 Score 70 70 69 66 60 92 56 93 75 a. Find the correlation coefficient: r = Round to 2 decimal places. b. The null and alternative hypotheses for correlation are: Ho: (? ;] = 0 H1 : 2 4 7 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. There is statistically insignificant evidence to conclude that there is a correlation between the time spent studying and the score on the final exam. Thus, the use of the regression line is not appropriate. There is statistically significant evidence to conclude that a student who spends more time studying will score higher on the final exam than a student who spends less time studying. There is statistically significant evidence to conclude that there is a correlation between the time spent studying and the score on the final exam. Thus, the regression line is useful. There is statistically insignificant evidence to conclude that a student who spends more time studying will score higher on the final exam than a student who spends less time studying. d. (Round to two decimal places) e. Interpret r: There is a 79% chance that the regression line will be a good predictor for the final exam score based on the time spent studying. Given any group that spends a fixed amount of time studying per week, 79% of all of those students will receive the predicted score on the final exam. 79% of all students will receive the average score on the final exam. There is a large variation in the final exam scores that students receive, but if you only look at students who spend a fixed amount of time studying per week, this variation on average is reduced by 79%. f. The equation of the linear regression line is: (Please show your answers to two decimal places)g. Use the model to predict the final exam score for a student who spends 10 hours per week studying. Final exam score = (Please round your answer to the nearest whole number.) h. Interpret the slope of the regression line in the context of the question: o For every additional hour per week students spend studying, they tend to Score on averge 2.44 higher on the final exam. As x goes up, y goes up. The slope has no practical meaning since you cannot predict what any individual student will score on the final. i. Interpret the y-intercept in the context of the question: o If a student does not study at all, then that student will score 60 on the final exam. o The average final exam score is predicted to be 60. The y-intercept has no practical meaning for this study. The best prediction for a student who doesn't study at all is that the student will score 60 on the final exam.Astudy was done to look at the relationship between number of vacation days employees take each year and dye number of sick days they take each year. The results of the survey are shown below. mmlllllll manna-amnion.\" a. Find the correlation coefficient: r = [:l Round to 2 decimal places. b. The null and alternative hypotheses for correlation are: Ho= m = 3.. m s a The p-value is: l:| [Hound to four decimal places} c. Use a level of significance of a = [Lilo to state the conclusion of the hypothesis test in the context of the study. 111ere 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 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 insignificant evidence to conclude that there is a correlation between the number of vacation days taken and the number of sick days taken. 111us, the use of the regression line is not appropriate. 111ere is statistically signicant evidence to conclude that an employee vmo takes more vacation days will take fewer sick days than an employee who takes fewer vacation days . d. :r-2 - ':] [Round to two decimal places} e. Interpret r2 : 45% of all employees will take the average number of sick days. There is a 45% chance that the regression line will be a good predictor for the number of sick days taken based on the number of vacation days taken. 111ere 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 4535. Given any group with a fixed number of vacation days taken, 45% of all of U'l-DS'E employees will take the predicted number of sick days. f. The equation of the linear regression line is: D = I (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 3 vacation days this 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 As x goes up, y goes down. For every additional vacation day taken, employees tend to take on average 0.38 fewer sick days. The slope has no practical meaning since a negative number cannot occur with vacation days and sick days. i. Interpret the y-intercept in the context of the question: o The y-intercept has no practical meaning for this study. o The average number of sick days is predicted to be 8. The best prediction for an employee who doesn't take any vacation days is that the employee will take 8 sick days. If an employee takes no vacation days, then that employee will take 8 sick days.ED! 3E A researcher found the correlation between age of death and number of cigarettes smoked per day to be 41.95. Based just on this information, the researcher can justly conclude that smoking causes early death. --true false Question 11 G 0/1 A study was done on smoking and lung capacity. 200 smokers took part in a study that asked them how many cigarettes a day they smoked and then measured their lung capacity. The correlation was found to ber = - 0.992 . Based solely on this study it can be concluded that smoking causes lung cancer. false o true Hint: Help. Question 12 0/1 pt A study of the CO2 concentration and global temperature data found that the correlation between CO2 concentration and global temperature was 0.993. Based on this correlation, it can be concluded that the increased level of CO2 concentration is causing global warming. o false o trueQuestion 13 Data was collected on the number of pairs of shoes people own and the number of miles they walk per week. r = 0.38 . Then 38% of the variation in miles walked can be explained by the linear relationship between the in the number of shoes owned and the miles walked. 62% is attributable to other factors. false o true