The accompanying data are a subset of data from the report “Great Jobs, Great Lives” (Gallup-PurdueIndex 2015 Report, gallup.com/reports/197144  /gallup-purdue index-report-2015.aspx, retrieved May 27, 2017). The data are approximate values read from a scatterplot. University students were asked if they agreed that their education was worth the cost. One variable in the table is the U.S. News and World Report ranking of the university in 2015. The other variable in the table is the percentage of students at the university who responded “strongly agree.”

University Ranking ..................... Percentage of Alumni Who Strongly Agree
28 ............................................................................. 53
29 ............................................................................. 58
30 ............................................................................. 62
37 ............................................................................. 55
45 ............................................................................. 54
47 ............................................................................. 62
52 ............................................................................. 55
54 ............................................................................. 62
57 ............................................................................. 70
60 ............................................................................. 58
65 ............................................................................. 66
66 ............................................................................. 55
72 ............................................................................. 65
75 ............................................................................. 57
82 ............................................................................. 67
88 ............................................................................. 59
98 ............................................................................. 75

a. Fit a linear regression model to predict the percentage of alumni who strongly agree that their education was worth the cost, using 2015 university ranking as a predictor.

b. Do the sample data support the hypothesis that there is a useful linear relationship between the percentage of alumni who strongly agree that their education was worth the cost and 2015 university ranking? Test the appropriate hypotheses using α = 0.05.