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Question text
Base your answer on the following scenario

A group of middle managers in a company are required to undergo a training programme aimed at improving their leadership abilities. A researcher wants to establish the effectiveness of the training programme. She tests each participant before the training commences on a questionnaire that measures the leadership ability of each participant as well as their score on a scale that measures self-esteem. After the training programme is completed, each participant is again tested for their leadership ability. The table below shows the results of the measurements.



Case

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

Gender

1

1

1

1

1

1

1

1

1

2

2

2

2

2

2

2

2

SelfEst

5

4

3

1

3

4

5

3

2

2

3

3

4

2

2

3

3

Lead1

5

4

3

3

4

6

5

4

4

4

5

4

5

1

2

3

6

Lead2

6

6

3

4

6

7

4

5

4

6

7

6

5

3

4

5

5

Key:

The variable Gender is coded with 1 = Male; 2 = Female.

SelfEst is a variable indicating self-esteem and was measured on a 5-point scale (ranging from 1=’low self-esteem’ to 5=’high self-esteem’).

Leadership ability was measured twice on a 7-point scale (with 1=’very low leadership ability’ up to 7=’very high leadership ability’). Lead1 indicates the measurement before the training programme, while Lead2 represents the measurement thereafter.

Assuming that the data is normally distributed and the variances do not differ significantly, which of the following tests are appropriate to test the following hypothesis?: The researcher wants to establish whether a significant difference exists between male and female participants in the level of self-esteem of the participants before the training begins. He decides to do statistical significance testing to a level of significance of α = 0.05.



a.
The chi-square (χ2) test for two variables.



b.
Pearson’s correlation statistic (r).



c.
The td test for two dependent groups