## Problem Description:

Harrigan University, a liberal arts university in the Midwest, aims to attract high-quality students, especially from its region. To assess its performance and concerns, Harrigan has collected data on 178 accepted applicants from recent years. The dataset contains various variables, including whether the applicant accepted Harrigan's offer, whether they enrolled in a rival university, their high school club involvement, varsity letters, GPA, SAT scores, and a closely guarded combined score used for ranking applicants. Harrigan is worried that they might not be attracting enough top-tier students and that many of these students are choosing to enroll at Harrigan's main rival.

### Solution:

**1. Acceptance Rates by Combined Score:
**

To assess the acceptance rate of applicants, a 95% confidence interval was calculated for the proportion of all accepted applicants. The results are as follows:

**For all acceptable applicants:**(0.5042081, 0.6496837)**Combined score less than 330:**(0.5720655, 0.8417591)**Combined score between 330 and 375:**(0.5062454, 0.7110038)**Combined score greater than 375:**(0.2128134, 0.4973896)

**2. Acceptance Rates by Combined Score Median:
**

A 95% confidence interval for the proportion of students with a combined score less than the median (356) who chose Harrigan's rival over Harrigan and for those with a combined score greater than the median was calculated:

**Combined score less than 356:**(0.62328, 0.8145404)**Combined score greater than 356:**(0.5002905, 0.7417287)

**3. Means and Differences in Means:
**

Confidence intervals for the mean combined score, high school GPA, and SAT scores for students who accept Harrigan's offer to enroll and for those who choose to enroll elsewhere were calculated. Additionally, confidence intervals for the differences in means were computed:

**Mean Difference:
**

**Combined score:**-25.96286**High school GPA:**-0.1702**SAT:**-7.87

**95% Confidence Intervals for Differences:
**

**Combined score:**(-36.55438, -13.37134)**High school GPA:**(-0.289718, -0.0506819)**SAT:**(-63.53431, 47.79431)

**4. Extracurricular Activities:
**

A 95% confidence interval for the proportion of students who decided to enroll at Harrigan and have been officers of at least two clubs and for those who have earned at least four varsity letters in sports was calculated:

**Officers of at least two clubs:**(0.4721607, 0.6317585)**Earned at least four varsity letters in sports:**(0.4730158, 0.6381147)

**5. School Size and Student Attraction:
**

To understand whether Harrigan is relatively more successful in attracting students from large high schools compared to small high schools, the data was divided into two categories based on the median high school size. A confidence interval was calculated to shed light on this issue:

**Large High Schools (Above Median):**-30.43117, -12.33073- This significant result (p value < 0.001) suggests that Harrigan might indeed be more successful in attracting students from larger high schools.

In conclusion, the analysis provides insights into Harrigan's admissions process. The university appears to be successful in attracting students who have been involved in extracurricular activities and from larger high schools. However, the university may need to work on improving its attraction of students with higher combined scores and SAT scores.