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PYC3714-25-S2
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A teacher investigates the effect of extra classes on the performance of pupils in mathematics. A group of 20 pupils receives the extra classes while a control group of 20 pupils receives singing lessons. For each of the 40 pupils the teacher calculates the increase or decrease in his or her mathematics performance by comparing the marks obtained in an examination before the extra classes to the marks obtained in an examination after the extra classes.
Which is the most appropriate research hypothesis for the teacher to test?
A teacher investigates the effect of extra classes on the performance of pupils in mathematics. A group of 20 pupils receives the extra classes while a control group of 20 pupils receives singing lessons. For each of the 40 pupils the teacher calculates the increase or decrease in his or her mathematics performance by comparing the marks obtained in an examination before the extra classes to the marks obtained in an examination after the extra classes.
Which is the appropriate test statistic to be calculated for the teacher to test the hypothesis (based on all the information provided in the case study)?
If the investigator is interested only in a change which is in a specific direction, it is appropriate to use a - - - - -.
In statistical hypothesis testing, the - - - - - is used to determine the - - - - - which is to be compared to the chosen - - - - - to make an inference regarding the status of the hypotheses.
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 on 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
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1
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2
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3
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4
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5
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6
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7
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8
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9
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10
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11
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12
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13
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14
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15
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16
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17
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Gender
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1
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1
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1
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1
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1
|
1
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1
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1
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1
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2
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2
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2
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2
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2
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2
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2
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2
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SelfEst
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5
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4
|
3
|
1
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3
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4
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5
|
3
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2
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2
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3
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3
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4
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2
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2
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3
|
3
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Lead1
|
5
|
4
|
3
|
3
|
4
|
6
|
5
|
4
|
4
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4
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5
|
4
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5
|
1
|
2
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3
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6
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Lead2
|
6
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6
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3
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4
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6
|
7
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4
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5
|
4
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6
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7
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6
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5
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3
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4
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5
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5
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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’).
Lead1indicates the measurement before the training programme, while
Lead2represents the measurement
thereafter.
The researcher wants to determine whether the workshop is effective by comparing the measurements on the measurement of leadership ability before the training programme with the measurements on this scale after the programme. Which of the following is an appropriate test statistic to calculate?
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 on 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
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1
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2
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3
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4
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5
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6
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7
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8
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9
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10
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11
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12
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13
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14
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15
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16
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17
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Gender
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1
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1
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1
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1
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1
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1
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1
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1
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1
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2
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2
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2
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2
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2
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2
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2
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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’).
Lead1indicates the measurement before the training programme, while
Lead2represents the measurement
thereafter.
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. Which of the following is the most appropriate way to express the hypotheses to be tested?
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 on 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
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1
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2
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3
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4
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5
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6
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7
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8
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9
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10
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11
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12
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13
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14
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15
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16
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17
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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’).
Lead1indicates the measurement before the training programme, while
Lead2represents the measurement
thereafter.
The researcher finds that the test statistic calculated yields a p-value of p = . What conclusion can be drawn about the training programme?
Whether the p value for directional or non directional testing on a hypothesis should be used depends on - - - - -.
What is the main difference between a z-test and a t-test when a single sample test for a mean is performed?
Two samples may be regarded as dependent when - - - - - -.
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 on 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
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1
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2
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3
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4
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5
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6
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7
|
8
|
9
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10
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11
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12
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13
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14
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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’).
Lead1indicates the measurement before the training programme, while
Lead2represents the measurement
thereafter.
In which of the following intervals would a test statistic (using the information taken from the case study) fall if it is calculated? (Use the absolute value of the calculated test statistic).