Question

Can someone please answer this question.

The following case studies require the use of a computer and software. Conduct all tests of hypotheses at the 5% significance level. Remember that homework assignments are individual work, and that even though you may discuss general solution procedures, the work you turn in must be your own 1. Ontario high school students must complete a minimum of six Ontario Academic Credits (OACs) to gain admission to a university in the province. Most students take more than six OACs because universities take the average of the best six in deciding which students to admit. Most programs at universities require high school students to select certain courses. For example, science programs require two of chemistry, biology, and physics. Students applying to engineering must complete at least two mathematics OACs as well as physics. In recent years, one business program began an examination of all aspects of its program, including the criteria used to admit students. Students are required to take English and calculus OACs, and the minimum high school average is about 85%. Strangely enough, even though students are required to complete English and calculus, the marks in these subjects are not included in the average unless they are in the top six courses in a student's transcript. To examine the issue, the registrar took a random sample of students who recently graduated with the BBA (bachelor of business administration degree). He recorded the university GPA (range 0 to 12), the high school average based on the best six courses, and the high school average using English and calculus and the four next best marks a. Is there a relationship between university grades and high school average using the best six OACs? b. Is there a relationship between university grades and high school average using the best four OACs plus calculus and English? c. Write a report to the university's academic vice president describing your statistical analysis and your recommendations.

Answer 1

Given the question has demanded the use of a computer and software, it should be accompanied by some data on which the processing could be done. Although, data is absent, I will try to address the questions asked.

a. Relationship between university grades and high school average using the best four OACs:

Let us first try to understand it figuritively. Relationships between two data sets can be estimated or understood using statistical correlation coefficients. Correlation, which means the relation between two, indicates how similar the two data are or if the follow the same trend in general, or how much similarity lies between the data. Do note that, correlation does not imply causality between the data sets. Now, let us come to the problem in this case study. In principle, students receiving higher average in high school should be academically good students and thus there is a high probability that they excel in university also, hence we can except higher grades from them in university. As a result the correlation between the average in high school and the grades at the university should be high.

Although, there is a point, which is important to note, that the high school average is being calculated using the best six OACs which may not include English and Calculus (proficiency in both subjects is assumed to be essential for Business Administration degree). This may result into those students being selected who did not score good in these two subjects but are enrolled in the BA degree at the university. This might result in them getting not particularly good grades in university and hence the correlation in this case might be less than in ques b.

b. Relationship between university grades and high school average using the best four OACs including English and Calculus:

In this case, the correlation is expected to be higher because we are giving priority to those studenst who have scored welll in English and Calculus. In other words, students having a higher high school average including English and Calculus are expected to get better grades in the BA degree. Thus a greater correlation is to be expected in this case.

c. So, the statistical analysis that is to be performed on the datasets is calculating correlation coefficients. There are multiple correlation coefficients which are easy to calculate/code in programs and also readily available in Statistical tools (like MATLAB statistics toolbox). Correlation coefficients (Pearson Correlation coefficient is a good choice) should be calculated for the datasets as mentioned in part a nd b. It is very likely that our hypothesis stands and we will get higher correlation coefficient in part b. Thus, it seems more profitable for the university to select the students based on their best 4 OACs plus calculus and english scores. This is what should be recommended to the vice president along with the data supporting the claim.