Question

Question 5.[15 marks] [Chapters 7 and 8] Data from a random sample of a recent large second semester stage 2 statistics course (STATS 20x) were collected. Below is some information on the variables collected. Variable Grade The student's final grade for the course: A, B. C, D Pass Whether the student passed the course: Yes, No Programme The programme the student is enrolled in: BA, BCom BSc, Other Sex The student's sex: Female, Male ผhether the student regularly attended class: Yes, No Attend The student's final exam mark (out of 100) Exam Test The student's mid semester test mark (out of 20) Assignment The student's assignment mark (out of 20) Diff The difference in a student's assignment and test mark (Assignment Test) Stage 1 The student's stage 1 grade: A, B, C (a) For each of the scenarios 1 to 5 below: I5 marks-1 mark for each scenario ] (i) Write down the name of the variable(s), given in the table above, needed to examine the question. (i) For each variable in (i) write down its type (numeric or categorical). (b) What tool(s) should you use to begin to investigate the scenarios 1 to 5 below? Write down the scenario number 1 to 5 followed by the appropriate tool. Hint: Refer to the blue notes in Chapter 1 in the Lecture Workbook. I5 marks- 1 mark for each scenario ] (c) Given that the underlying assumptions are satisfied, which form of analysis below should be used in the investigation of each of the scenarios 1 to 5 below? Write down the scenario number 1 to 5 followed by the appropriate Code A to F. (See page 4.) IS marks-1 mark for each scenario ] Scenario 1 Is there a relationship between sex and the exam mark a student achieves? Scenario 2: Is there a difference between the proportion of attending students who pass the course and the proportion of non-attending students who pass the course? Scenario 3: On average do we expect a student's assignment mark to be different from their test mark? Scenario 4: Is there a link between a student's test mark and the programme they are enrolled in? Scenario 5: Does a student's assignment mark depend on their Stage 1 grade?

Answer 1

This is a simple problem regarding analysing the nature of the variables involved in the question and providinig details of the analytics tools for the same.

1). The variable types and the reason for them being so is provided below

		Variable type
S.No.	Variable name	Numerical	Quantitative	Why ?
1	Grade		√	These are NOT countable. They can only be described by attributes
2	Pass		√	These are NOT countable. They can only be described by attributes
3	Programme		√	These are NOT countable. They can only be described by attributes
4	Sex		√	These are NOT countable. They can only be described by attributes
5	Attend		√	These are NOT countable. They can only be described by attributes
6	Exam	√		These variables are countable and have distinct numerical value attached to each of its data point
7	Test	√		These variables are countable and have distinct numerical value attached to each of its data point
8	Assignment	√		These variables are countable and have distinct numerical value attached to each of its data point
9	Diff	√		These variables are countable and have distinct numerical value attached to each of its data point
10	Stage 1		√	These are NOT countable. They can only be described by attributes

The scenario are provided and the statisitcal method and he relevant tool to implement it are shown below

		Statistical tool used
Scenario number	Scenario requirement	Statistical method used	Statisitcal tool used	Why ?
1	To check if there is any relationship between sex type and exam marks	Correlation analysis	Correlation analysis	It will tell us the relationship between the data sets for different sex types. A correlation of 1 will tell us that both sex types are completely related and ne can be given by other. Similarly ,a correlation of 0 inidcates no relationship
2	To check if there is a difference between proportions of students passing the exam while attending and while not attending	Hypothesis testing	Difference in two sample proportion testing	Hypothesis testing for difference in sample prooprtion means will let us know if there is a differnece in the sample proportion means between two groups with a certain level of confidence.
3	to check if a students assignment marks are different from test marks	Hypothesis testing	z score testing for Difference in two sample means	Hypothesis testing will let us know if there is a differnece in the sample means between two gropus of assignment marks and test marks significiently with a certain level of confidence.
4	To check if there is a link between students' test marks and the type of programme they choose	Regression Analysis	Hypothesis testing for coefficient of the independent variable	It will test if the slope/ coefificent of the stage 1 grades variable is non zero or not siginificently. It it is so ,it will mean that since it is non zero, both will have a relationship with the coeffiicent defining the rate of change of assignment mrks with unit change in stage 1 grades. Since the grades are qualitiative ,we will have to make use of dummy variable concept.
5	To check if a students assignment marks are dependent on stage 1 grades