Harrigan University Report
Introduction and Problem Statement:-
A liberal Arts University in the Midwest, the Harrigan University wants the best quality students to enrol in their University, especially from its region of the country. The selection procedure at Harrigan is based on certain criteria, namely, the number of high school clubs the applicant has served as an officer in, number of varsity letters that the applicant has earned, the applicant’s high school GPA and the applicant’s combined SAT score, apart from others. The derivation of the combined scored is basically a weighted average of the above mentioned components.
Harrigan University is concerned that it is not getting enough of the best students and furthermore it is concerned that most of its selected best students opt for Harrigan’s main rival.
Based on the sample information of 178 students(from all acceptable students from past several years), we need to determine whether Harrigan University has a legitimate concern.
Summary/Results:-
1. Find a 95% confidence interval for the proportion of all acceptable applicants who accept Harrigan's invitation to enroll. Do the same for all acceptable applicants with a combined score less than 330; with a combined score between 330 and 375; with a combined score greater than 375. (Note that 330 and 375 are approximately the first and third quartiles of the Score variable.)
ANSWER:
95% confidence interval for the proportion of all acceptable applicants
1. who accept Harrigan’s invitation to enrol is
50.56 % to 65.17 %
2. with a combined score less than 330 is
59.18% to 86.27%
3. with a combined score between 330 and 375 is
52.06% to 72.38%
4. with a combined score greater than 375 is
19.68% to 48.50%
2. Find a 95% confidence interval for the proportion of all acceptable students with a combined score less than the median (356) who choose Harrigan's rival over Harrigan. Do the same for those with a combined score greater than the median.
ANSWER:
A liberal Arts University in the Midwest, the Harrigan University wants the best quality students to enrol in their University, especially from its region of the country. The selection procedure at Harrigan is based on certain criteria, namely, the number of high school clubs the applicant has served as an officer in, number of varsity letters that the applicant has earned, the applicant’s high school GPA and the applicant’s combined SAT score, apart from others. The derivation of the combined scored is basically a weighted average of the above mentioned components.
Harrigan University is concerned that it is not getting enough of the best students and furthermore it is concerned that most of its selected best students opt for Harrigan’s main rival.
Based on the sample information of 178 students(from all acceptable students from past several years), we need to determine whether Harrigan University has a legitimate concern.
Summary/Results:-
1. Find a 95% confidence interval for the proportion of all acceptable applicants who accept Harrigan's invitation to enroll. Do the same for all acceptable applicants with a combined score less than 330; with a combined score between 330 and 375; with a combined score greater than 375. (Note that 330 and 375 are approximately the first and third quartiles of the Score variable.)
ANSWER:
95% confidence interval for the proportion of all acceptable applicants
1. who accept Harrigan’s invitation to enrol is
50.56 % to 65.17 %
2. with a combined score less than 330 is
59.18% to 86.27%
3. with a combined score between 330 and 375 is
52.06% to 72.38%
4. with a combined score greater than 375 is
19.68% to 48.50%
2. Find a 95% confidence interval for the proportion of all acceptable students with a combined score less than the median (356) who choose Harrigan's rival over Harrigan. Do the same for those with a combined score greater than the median.
ANSWER: