A researcher would like to conduct a study related to self-esteem in a university. The researcher would like to examine

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A researcher would like to conduct a study related to self-esteem in a university. The researcher would like to examine two objectives in his study. First, he would like to examine whether the coaching programme provided by the university will improve the level of self-esteem among the university students. Second, he would like to study the relationship between student academic performance (CGPA) and students’ self-esteem in a university. Thirty samples of students from the first year were taken for the study. The researcher has collected the data for a few variables: gender, academic performance, and self-esteem test score.
The study is divided into two parts. First, the student must answer the self-esteem test before attending the coaching programme. Second, the researcher will request the same thirty students to attend a three-month coaching programme. Upon completing the coaching program, students are requested to answer the self-esteem test again. The results for thirty student’s data are in the following Table 1:
Table 1: Self-esteem Scores among Students.
Student
Gender
CGPA
Self-esteem Coaching (Programme)
Self-esteem Score
(Before Attend Coaching)
A
Self-esteem Score (After Attend Coaching)
B
1
Male
2.10
12
30
2
Female
4.00
22
36
3
Male
2.30
12
28
4
Male
2.40
14
28
5
Female
3.80
34
40
6
Female
3.90
32
40
7
Male
2.70
25
28
8
Male
3.10
24
28
9
Male
2.90
22
28
10
Male
3.00
14
26
11
Male
2.50
12
24
12
Female
3.20
32
40
13
Male
2.60
20
32
14
Female
3.40
32
38
15
Female
3.50
32
40
16
Female
3.60
34
40
17
Female
3.70
30
40
18
Male
2.80
28
38
19
Female
3.30
30
38
20
Male
2.20
18
36
21
Female
3.90
34
40
22
Female
3.30
29
38
23
Female
3.50
31
40
24
Male
3.10
27
34
25
Male
2.90
28
34
26
Male
3.20
30
40
27
Female
3.10
32
38
28
Male
3.00
30
40
29
Female
3.90
36
40
30
Male
2.80
28
38
Remarks:
Range of CGPA: 0.00 to 4.00
Range of self-esteem scores: 0 to 40
0 to 7 Very Low
8 to 15 Low
16 to 23 Moderate
24 to 31 High
32 to 40 Very High
Question 1: Descriptive statistics problem solving (30%)
Based on the data in Table 1, answer the following questions based on self-esteem scores before and after students attended the coaching programme for the whole samples. Show your detailed workings clearly and coherently.
Calculate the mean. (4 marks)
Calculate the median. (4 marks)
Calculate the mode. (4 marks)
Calculate the variance. (4 marks)
Calculate the standard deviation. (7 marks)
Construct the frequency distribution for range of self-esteem scores before attending the coaching programme. (7 marks)
Question 2: Inferential statistics report (20%)
Based on the sample data from table 1, you are required to answer the following questions:
1. Perform hypothesis testing to determine whether there is a difference in the means of the distribution in self-esteem scores before and after attending the coaching programme. The hypothesis testing is performed with a level of significance α equal to 5 percent and report the hypothesis findings. (10 marks)
2. Analyse the relationship between students’ academic performance (CGPA) and self-esteem scores for students who completed the coaching programme. Compute the coefficient of correlation for these data. Describe the relationship between two variables. Report the findings of the relationship between two variables. (10 marks)