Juniors at New City High School were offered the opportunity to participate in a free after-school tutoring program to help them prepare for the SAT exam. A total of 40 one-hour tutoring sessions were offered, and all students were invited drop in to any number of sessions. Students who did participate were asked to sign in, and the school kept track of who participated and for how many hours.

Principal Parker is trying to decide whether to keep investing resources in the free program and wants to know if it is having a positive impact on students. After the SAT exams were completed, she took a random sample of 25 New City HS juniors. She put together a data set (in the "Tutoring" tab) including observations of the following for each sampled student: (1) combined SAT score in critical reading and math, (2) grade point average (GPA), and (3) number of hours spent in the free SAT prep tutoring program. She has asked you to investigate whether participation in the tutoring program is associated with higher SAT scores, while accounting for the potential impact of a student's GPA on SAT score.

(a) What are the null and alternative hypotheses for the relationship between the dependent variable and the other independent variable? State them using notation, and in words. (b) Interpret the slope coefficient for the other independent variable, in context. (c) What are the t statistic and p value for this hypothesis test? Interpret the p-value. (d) Do you have evidence to reject the null hypothesis? If so, at what level? State your conclusion.

Variables Operational Form GPA and TV hours Description positive numbers from 1-60 Name points, ranging from 2.0-4.0 subject student identification number high_sch_gpa student's high school GPA hours , ranging from 0-37 tv tv hours of television watched by student per week subject high_sch_GPA 2.2 3.3 3.5 3.1 3.5 3.6 3 3 4 2.3 3.5 3.3 3.2 mmmMmmMMM Mmmmmmmmmsmiteumm gTutoring hours, GPA, and SAT score data Variables Name Description Operational Form student sat score gpa tutoring hours student student identification number positive numbers from 1-25 980 3. 15.0 sat score combined SAT score points, ranging from 400-1600 1550 3.9 22.0 gpa high school grade point average points, ranging from 1.0-4.0 1100 3.6 0.0 tutoring hours hours spent in tutoring program hours, ranging from 0-40 840 2.9 10.0 380 1.9 0.0 770 3.5 15.0 850 3.0 5.0 910 2.6 10.0 1300 3.9 15.0 1400 3.5 10.0 680 3.0 4.0 930 3.3 5.0 1010 3.5 8.0 1230 3.4 10.0 1120 2.9 26.0 690 3.2 5. 990 3.8 0.0 790 3.1 12.0 830 3.0 7.0 1020 3.0 22.0 1200 3.7 5.0 500 2.7 0.0 1260 2.9 20.0 740 2.9 5.0 1410 3.2 20.0