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Background BSB123 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...

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Background
BSB123 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[4]

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 29.4 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.)
(3 marks)
  1. In order to investigate gender difference in exam performance you conduct separate two-sample t-tests. (Conduct your tests at a = 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.
(1 mars)
(b) Considering single degree students only, test if there is any gender difference in exam performance.
(1 mark)
(c) Considering double degree students only, test if there is any gender difference in exam performance.
(1 mark)
(d) Present your findings in parts (a), (b) and (c) using appropriate graph(s), and discuss any important observation(s).
(3 marks) [1] Buckley, Sarah, "Gender and sex differences in student participation, achievement and engagement in mathematics" XXXXXXXXXXSource: http://research.acer.edu.au/learning_processes/18 [2] American Psychological Association Press Release (April 29, XXXXXXXXXXSource: http://www.apa.org/news/press/releases/2014/04/girls-grades.aspx [3] The final exam contains short answer questions, assessing all major lecture topics. [4] The survey was conducted around Week 11, and the maximum number of lectures attended was therefore 10.
Answered Same DayDec 27, 2021

Solution

David answered on Dec 27 2021
67 Votes
GSN403 Understanding Data
1
Factors affecting exam performance in Data Analysis
Background
BSB123 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
usiness. 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 Attendance4
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 29.4 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.)

1 Buckley, Sarah, "Gender and sex differences in student participation, achievement and engagement in mathematics" (2016) Source:
http:
esearch.acer.edu.au/learning_processes/18
2 American Psychological Association Press Release (April 29, 2014). Source: http:
www.apa.org/news/press
eleases/2014/04/girls-
grades.aspx
333 The final exam contains short answer questions, assessing all major lecture topics.
4 The survey was conducted around Week 11, and the maximum number of lectures attended was therefore 10.
2
(3 marks)
Null hypothesis: The average final exam mark in 2015 in more than or equal to the average final
exam mark in 2014.
Alternate hypothesis: The average final exam mark in 2015 in less than the average final exam
mark in 2014.
Level of significance = 0.05
Average of the final exam marks of 694 students = 28.76
Standard deviation = 12.32
Test statistic is as follows:

̅




The critical value is -1.64.
Since, the critical value is greater calculated value of z, and then we do not reject the null
hypothesis.
Hence, the average final exam score in 2015 is greater than the average final exam score in 2014.
2. In order to investigate gender difference in exam performance you conduct separate two-
sample t-tests. (Conduct your tests at  = 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.
(1 marks)
Null hypothesis: There is no difference in the average exam performance between female
and male students.
Alternate hypothesis: There is a difference in the average exam performance between female
and male students.
F M
n 354 340
Mean 29.71 27.78
3
Standard
Deviation 12.19 12.39

( )
√( )



( )
The critical value of Z is 1.96.
Since, the critical value is less than the calculated z value, we reject the null hypothesis.
Hence, there is a significant difference in the average exam performance between female
and male students.
(b) Considering single degree students only, test if there is any gender difference in exam
performance.
(1 mark)
Null hypothesis: There is no difference in the average exam performance between female
and male students of single degree students.
Alternate hypothesis: There is a difference in the average exam performance between female
and male students single degree students.
F M
n 216 242
Mean 27.12 27.12
Standard
Deviation 11.32 12.57

( )
√( )



( )
The critical value of Z is 1.96.
Since, the calculated value is less than the critical z value, we do not reject the null
hypothesis. Hence, there is no significant difference in the average exam performance
etween female and male students of single degree students.
(c) Considering double degree students only, test if there is any gender difference in exam...
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