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 87 66 68 63 a. Find the correlation coefficient: r : = : Round to 2 decimal places. b. The null and alternative hypotheses for correlation are: HEN-=0 H.-ao_ The p-value is: : 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 = (Round to two decimal places) e. Interpret r2 : 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 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 0 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 : I I Round to 2 decimal places. b. The null and alternative hypotheses for correlation are: Ho=-=0 H1: 7A0 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 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 = I (Round to two decimal places) e. Interpret 7'2\": O 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%. 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 0 Greater than a The p-value leads to a decision to O Reject Ho 0 Accept Ho Q Do Not Reject Ho