0 Question 33 v 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 0 8 5 6 7 13 5 3 Score 46 71 63 66 83 86 59 69 a. Find the correlation coefficient: r : C] Round to 2 decimal places. b. The null and alternative hypotheses for correlation are: Ho:-=0 H1:- 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. 0 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. 0 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. 0 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. 0 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. d. r2 = C] [Round to two decimal places) e. Interpret r2 : O 71% of all students will receive the average score on the final exam. 0 There is a 71% chance that the regression line will be a good predictor for the final exam score based on the time spent studying. 0 Given any group that spends a fixed amount of time studying per week, 71% of all of those students will receive the predicted score on the final exam. 8 9 pts '01 8 99 6) Details O 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 71%. f. The equation of the linear regression line is: A y = g. Use the model to predict the final exam score for a student who spends 7 hours per week studying. Final exam score = C] (Please round your answer to the nearest whole number.) h. Interpret the slope of the regression line in the context of the question: + '3: (Please show your answers to two decimal places) O The slope has no practical meaning since you cannot predict what any individual student will score on the final. 0 For every additional hour per week students spend studying, they tend to score on averge 3.21 higher on the final exam. O As x goes up, y goes up. i. Interpret the y-intercept in the context of the question: 0 If a student does not study at all, then that student will score 50 on the final exam. 0 The best prediction for a student who doesn't study at all is that the student will score 50 on the final exam. O The average final exam score is predicted to be 50. O The y-intercept has no practical meaning for this study