The Venn diagram below shows the students in Ms. Morris's class. The diagram shows the memberships for the Tennis Club and the Soccer Club. A student from the class is randomly selected. Let denote the event "the student is in the Tennis Club." Let denote the event "the student is in the Soccer Club." The outcomes for the event are listed in the circle on the left. The outcomes for the event are listed in the circle on the right. Note that Linda is outside the circles since she is not a member of either club. Answer Submitted: (a) Find the probabilities of the events below. Write each answer as a single fraction. (b) Select the probability that is equal to . Correct Answer: (a) Find the probabilities of the events below. Write each answer as a single fraction. (b) Select the probability that is equal to . P(A)= P(B)= P(A and B)= P(A) * P(B/A)=1/6

Padma completed her doctoral degree and has taken a position as an assistant professor at a local university. She was given the following performance measures for her new position. Identify whether these goals are long or short term. Interact in a fair and impartial way with students. Promote and access student academic achievement. Counsel students within the norms of society and the regulations of the college. Motivate students. Effectively plan and organize lectures and labs in accordance with the college course outlines. Report class attendance in accordance with the college policy and procedure. Serve on academic committees as assigned. Make progress toward tenure necessary at her university.

The Scholastic Aptitude Test (or SAT) is a standardized college entrance test that is used by colleges and universities as a means for making admission decisions. The critical reading and mathematics components of the SAT are reported on a scale from 200 to 800. Several universities believe these scores are strong predictors of an incoming student’s potential success, and they use these scores as important inputs when making admission decisions on potential freshman. The tile RugglesCollege contains freshman year GPA and the critical reading and mathematics SAT scores for a random sample of 200 students who recently completed their freshman year at Ruggles College. Develop an estimated multiple regression equation that includes critical reading and mathematics SAT scores as independent variables. How much variation in freshman GPA is explained by this model? Test whether each of the regression parameters β0, β1, and β2, is equal to zero at a 0.05 level of significance. What are the correct interpretations of the estimated regression parameters? Are these interpretations reasonable? Using the multiple linear regression model you developed in part (a), what is the predicted freshman GPA of Bobby Engle, a student who has been admitted to Ruggles College with a 660 SAT score on critical reading and at a 630 SAT score on mathematics? The Ruggles College Director of Admissions believes that the relationship between a student’s scores on the critical reading component of the SAT and the student’s freshman GPA varies with the student’s score on the mathematics component of the SAT. Develop an estimated multiple regression equation that includes critical reading and mathematics SAT scores and their interaction as independent variables. How much variation in freshman GPA is explained by this model? Test whether each of the regression parameters β0, β1, β2, and β3 is equal to zero at a 0.05 level of significance. What are the correct interpretations of the estimated regression parameters? Do these results support the conjecture made by the Ruggles College Director of Admissions? Do you prefer the estimated regression model developed in part (a) or part (c)? Explain. What other factors could be included in the model as independent variables?

Padma completed her doctoral degree and has taken a position as an assistant professor at a local university. She was given the following performance measures for her new position. Identify whether these goals are long or short term. A. Interact in a fair and impartial way with students. B. Promote and access student academic achievement. C. Counsel students within the norms of society and the regulations of the college. D. Motivate students. E. Effectively plan and organize lectures and labs in accordance with the college course outlines. F. Report class attendance in accordance with the college policy and procedure. G. Serve on academic committees as assigned. H. Make progress toward tenure necessary at her university.