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 11 15 5 3 13 1 7 0 Score 61 84 98 78 54 37 66 68 63 a. Find the correlation coefficient: r : I I Round to 2 decimal places. b. The null and alternative hypotheses for correlation are: Btu-:0 H1=-%70 The p-value is: I I {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 there is a correlation between the time spent studying and the score on the final exam. Thus, the regression line is useful. Q 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. Q 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. 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. d. r2 =I I (Round to two decimal places) e. Interpret 7'2 : Q There is a 76% 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, 76% of all of those students will receive the predicted score on the final exam. 0 76% of all students will receive the average score on the final exam. 0 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 76%. a f. The equation of the linear regression line is: g} = | +| Ea: (Please show your answers to two decimal places} g. Use the model to predict the final exam score for a student who spends 7 hours per week studying. Final exam score = l | (Please round your answer to the nearest whole number.) h. Interpret the slope of the regression line in the context of the question: 0 For every additional hour per week students spend studying, they tend to score on averge 2.37 higher on the final exam. 0 As x goes up, y goes up. 0 The slope has no practical meaning since you cannot predict what any individual student will score on the final. 1. Interpret the y-intercept in the context of the question: 0 If a student does not study at all, then that student will score 57 on the final exam. 0 The best prediction for a student who doesn't study at all is that the student will score 57 on the final exam. O The average final exam score is predicted to be 57. O The y-intercept has no practical meaning for this study. Listed below are paired data consisting of amounts spent on advertising (in millions of dollars) and the profits (in millions of dollars). Determine if there is a significant linear correlation between advertising cost and profit . Use a significance level of 0.05 and round all values to 4 decimal places. Advertising Cost Profit 18 28 18 19 18 18 33 35 Ho:p=0 Ha:p:0 Find the Linear Correlation Coefficient r: Find the p-value p-value = The p-value is 0 Less than (or equal to) a. O Greater than a The p-value leads to a decision to O Reject Ho 0 Accept Ho 0 Do Not Reject Ho The conclusion is Q There is a significant negative linear correlation between advertising expense and profit. 0 There is a significant positive linear correlation between advertising expense and profit. Q There is a significant linear correlation between advertising expense and profit. 0 There is insufficient evidence to make a conclusion about the linear correlation between advertising expense and profit. A study was done to look at the relationship between number of lovers college students have had in their lifetimes and their GPAs. The results of the survey are shown below. Lovers 0 2 O 2 2 3 7 GPA 3.2 3.4 3.3 2.9 2.9 3.5 2.1 a. Find the correlation coefficient: r : Round to 2 decimal places. b. The null and alternative hypotheses for-correlation'are: Ha=-= H1:- #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. Q There is statistically significant evidence to conclude that a student who has had more lovers will have a lower GPA than a student who has had fewer lovers. 0 There is statistically insignificant evidence to conclude that a student who has had more lovers will have a lower GPA than a student who has had fewer lovers. 0 There is statistically significant evidence to conclude that there is a correlation between the number of lovers students have had in their lifetimes and their GPA. Thus, the regression line is useful. 0 There is statistically insignificant evidence to conclude that there is a correlation between the number of lovers students have had in their lifetimes and their GPA. Thus, the use of the regression line is not appropriate. d. r2 = (Round to two decimal places) e. Interpret r2 : 0 Given any group of students who have all had the same number of lovers, 57% of all of these studetns will have the predicted GPA. O 57% of all students will have the average GPA. Q There is a large variation in students' GPAs, but if you only look at students who have had a fixed number of lovers, this variation on average is reduced by 57%. 0 There is a 57% chance that the regression line will be a good predictor for GPA based on the number of lovers a student has had. f. The equation of the linear regression line is: y"! = | | +i in: (Please show your answers to two decimal places) g. Use the model to predict the GPA of a college student who as had 4 lovers. GPA = | | {Please round your answer to one decimal place.) h. Interpret the slope of the regression line in the context of the question: 0 The slope has no practical meaning since a GPA cannot be negative. 0 For every additional lover students have, their GPA tends to decrease by 0.15. Q As X goes up, y goes down. i. Interpret the yintercept in the context of the question: 0 The best prediction for the GPA of a student who has never had a lover is 3.39. O The y-intercept has no practical meaning for this study. 0 If a student has never had a lover, then that student's GPA will be 3.39. O The average GPA for all students is predicted to be 3.39