Introduction to Statistics Assignment -
Instructions - This assignment tests your basic statistical modelling skills, using spreadsheet software as well as your awareness of the reality of how probability calculations, estimation and regression work in practice. Your answers are to be presented in an essay/report format, for which you will use a word processor. In writing your report, please:
- state and explain all assumptions, on which your answers are based;
- clearly indicate your answer/recommendations
- support any answers with the appropriate calculations to arrive at the answer
- no evidence of use of excel will result in a fail mark for this assignment and therefore the coursework component of the module;
- include selected printouts of formulae underlying computed values. Failure to demonstrate you have created appropriate formulations on excel will be severely penalised. Despite the fact that you will be submitting the Excel file as well, your report is a stand-alone document, meaning a reader should not be required to look at the Excel file to understand your analysis, findings and recommendations
- please note that adequate usage of the excel calculations in the report is important. This means that the key data/findings need to be included in the report and appropriate referencing needs to be done, i.e. the relevant cell/table/range in the relevant tab of the excel file mentioned at the point of the report when it should be consulted.
Question 1: A statistician is trying to find whether there is a relationship between the number of hours of study and exam results, or whether exam results are random and collected data for two subjects which were recently examined. The data collected is summarised in the table below:
|
Student
|
Subject 1 Study Hours
|
Subject 1 Exam Grade
|
Subject 2 Study Hours
|
Subject 2 Exam Grade
|
|
1
|
25
|
80
|
34
|
86
|
|
2
|
5
|
8
|
44
|
38
|
|
3
|
18
|
16
|
45
|
100
|
|
4
|
29
|
87
|
3
|
10
|
|
5
|
17
|
95
|
33
|
61
|
|
6
|
39
|
90
|
50
|
62
|
|
7
|
49
|
84
|
17
|
60.5
|
|
8
|
25
|
82
|
43
|
95
|
|
9
|
6
|
35
|
45
|
39
|
|
10
|
22
|
58
|
38
|
24
|
|
11
|
37
|
71
|
11
|
61
|
|
12
|
31
|
89
|
34
|
85
|
|
13
|
18
|
57
|
3
|
19
|
|
14
|
5
|
9.5
|
31
|
55
|
|
15
|
45
|
22
|
44
|
46.5
|
|
16
|
4
|
10
|
17
|
33
|
|
17
|
17
|
23
|
39
|
50.5
|
|
18
|
16
|
74
|
45
|
96
|
|
19
|
29
|
55
|
0
|
12
|
|
20
|
22
|
29
|
15
|
87
|
|
21
|
28
|
69.5
|
42
|
36
|
|
22
|
6
|
27
|
10
|
32.5
|
|
23
|
4
|
8
|
38
|
66
|
|
24
|
21
|
14
|
29
|
33
|
|
25
|
4
|
23
|
49
|
76
|
|
26
|
12
|
39.5
|
19
|
61
|
|
27
|
24
|
26
|
49
|
94
|
|
28
|
31
|
77
|
14
|
46
|
|
29
|
38
|
24.5
|
33
|
29
|
|
30
|
5
|
13
|
14
|
67.5
|
Required:
a) Summarise the distribution of the grades for both exams, according to the data given. Discuss the key characteristics of the data.
b) Construct a 95% confidence interval for the exam marks for each of the subjects. Is there a significant difference between them?
c) By constructing a regression model for each of the subjects, indicate for which does study hours have a higher impact on exam grades. Do you think this result is significant?
d) For the best regression model in the previous question, identify whether a better model can be developed by splitting the data into students who study more than 20 hours versus students that study less than 20 hours.
e) Without further calculations, discuss whether you believe the data collected is biased or unbiased and if biased what actions should have been taken to avoid it happening.
Question 2: Tab 1 of the attached excel file called "Data File IF1202 CW March19" contains employment data for all states in the United States of America. The Federal Government is trying to decide whether to implement countrywide policies to increase employment in the female population and has asked you to analyse the data collected.
Required:
a) Summarise the distribution of employment for both the male and female populations in the USA.
b) Identify whether there is evidence that the average female employment rate is different from 68%.
c) Based on this sample, provide a 98% confidence interval for both male and female employment, and comment on the outcome.
d) Including a justification for the choice of significance level, identify whether there is evidence that employment is higher among the male than the female population.
e) Discuss whether a decision on implementing the above mentioned policies can be made solely based on this analysis and if not, what else should be considered.
Question 3: You have been asked by a recruitment consultant to analyse the data on salary and what affects an employee's salary that they have collected, which is contained in Tab 2 of the attached excel file called "Data File IF1202 CW March19".
Required:
a) Prepare a summary table with the correlations between all the variables and discuss which variables are highly correlated and which are not.
b) Construct a multiple regression model with all independent variables and clearly indicate your regression equation;
c) Indicate and justify which variables are significant and non-significant in the regression model and compare with your answer to part b) above;
d) Construct another multiple regression model including only the significant variable from the model in c) above and discuss whether it is a better model or not.
e) Indicate and justify whether you believe there is evidence of gender inequality in salaries for the data collected.
Attachment:- Assignment Files.rar