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Case Harrigan University
Harrigan University is liberal arts university in the Midwest that attempts to attract the highest-quality students, especially from its region of the country. It has gathered data on 178 applicants who were accepted by Harrigan (a random sample from all acceptable applicants over the past several years). The variables are: Accepted: whether the applicant accepts Harrigan’s offer to enroll Main Rival: whether the applicant enrolls at Harrigan’s main rival university. HSCluns: number of high school clubs applicant served as an officer HSSports: number of varsity letters applicant earned HSGPA: applicant’s high school GPA HSPctile: applicant’s percentile(in terms of GPA) in his or her graduating class HSSize: number of students in applicant’s graduating class SAT: applocant’s combined SAT score CombinedScore: a combined score for the applicant used by Harriigan to ramk applicants 1 The derivation of the combined score is a closely kept secret by Harrigan, but it is basically a weighted average of the various components of high school performance and SAT. Harrigan is concern that it is not getting enough of the best students, and worse yet, it is concerned that many of these best students are going to Harrigan’s main rival. Solve the following problems and then, based on your analysis, comment on whether Harrigan appears to have a legitimate concern. a. Find a 95% confidence interval for the proportion of all applicants with a combined score less than 330(which is approximately the first quartile of the Score variable) who accept Harrigan’s invitation to enroll( Accepted = Yes); b Find a 95% confidence interval for the proportion of all applicants with a combined score (CombinedScore) between 330 and 375 who accept Harrigan’s invitation to enroll (Accepted = Yes); c Find a 95 confidence interval for the proportion of all applicants with a combined (CombinedScore) greater than 375 (which is approximately the third quartiles of the Score...
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