Question

Data Analysis is designed to build a strong foundation for development of statistical literacy and statistical thinking. Both are essential for business success and further studies in business. Recent research showed that “On average for 15-year-old Australian students, females achieved at a significantly lower level than male students (in mathematics)” (p.2, Buckley 2016) 1 . However, there is also research evidence that “Despite the stereotype that boys do better in math and science, girls have made higher grades than boys throughout their school years for nearly a century” (APA 2014)2 . The Head of School funds a research study to investigate gender differences in, and other factors influencing, exam performance in Data Analysis. Data are collected on the following variables from a sample of 694 students enrolled in the unit in 2015.

• Final exam mark (out of 60)3

• Gender • Degree Type

• Country of Citizenship

• Lecture Attendance

You are appointed as the research analyst to examine the data and report key findings to the project officer. The dataset is contained in the file: Exam Results.xlsx. The project officer sets the following tasks to guide your investigation.

Task 1 (t-tests) 1. In 2014 the average final exam mark was 29.6 out of 60. You want to test at 5% if the average exam mark in 2015 has decreased. (Include all six steps of hypothesis testing.)

2. In order to investigate differences in exam performance you conduct separate two-sample t-tests. (Conduct your tests at α = 5%.)

(a) Considering the whole sample of 694 students, test if there is a difference in the average exam performance between female and male students.

(b) Test if there is a difference in the average exam performance between single degree and double degree students.

(c) Considering both single and double-degree students, test if there is any gender difference in exam performance.

(d) Present your findings in parts (a), (b) and (c) using appropriate graph(s), and discuss any important observation(s).

You plan to develop regression models to investigate the factors that influence students’ final exam performance. However, you are not sure how to handle the country of citizenship variable. After further discussion and based on international standardised tests, you and your project officer believe that East Asian students tend to have stronger maths background, and decide to create three categories: Australian, East Asian and others, to recode this variable. You also agree that East Asian students should include those from China, Japan, Korea, Taiwan and South East Asian countries, and that students from New Zealand are not classified as Australian.

You conduct several regressions as well as a stepwise regression according to the following procedure:

Step 1: All variables independently (SLR) with the dependent variable

Step 2: Gender and Degree Type (MLR)

Step 3: Gender, Degree Type and Country of Citizenship (MLR)

Step 4: Gender, Degree Type, Country of Citizenship and Lecture Attendance (MLR)

(a) Present the regression output for each of the regressions in a table noting the coefficients, assessing the adequacy of the model and the p-value of the model and the coefficients individually.

(b) Based on the regression output obtained in Step 4, answer the following questions: • Which models are significant? • For the model defined as Step 4: interpret the regression coefficients and comment on their statistical significance. Is this a useful model in being able to interpret a students mark in the final examination?

Country of Citizenship Australia Australia Australia Australia Australia Australia Australia Australia Australia Australia Australia Australia Australia Australia Australia Australia Australia Australia Australia Australia Australia Australia Australia Australia Australia Australia Australia Australia Australia Australia Korea, (Sth) Republic Of Australia Australia Australia Australia Australia Australia Australia Lecture Attendance 10 Gender Degree Type Double Single Single Single Single Single Single Single Single Single Single Single Single Double Single Single Single Single Double Single Double Single Single Single Single Single Single Single Single Single Single Single Single Single Single Single Single Single EXAM MARK 25 32 25.5 22.5 20 21.5 20.5 32.5 41.5 18.5 38.5 52 30 27.5 15 21.5 20.5 12.5 10 33.5 27.5 35.5 16 17.5 16 24.5 35.5 18.5

Answer 1