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Question
For your sample, determine whether there is a difference between their satisfaction with their jobs and their satisfaction with their incomes.
Be sure to use the proper df and show all the steps of calculations, including the test statistic.
Include an explanation of how the critical value was determined. Explain why you chose that specifict-test.
In addition, interpret the results of the analyses, focusing on the similarities and differences between using a pairedt-test and an independentt-test.
Name
Age
Height
(inches)
Gender
Years of college
Political affiliation
Hours of work per week
Satisfaction with job
Satisfaction with income
Satisfaction with economy
Jessica
25
67
F
4
R
40
5
5
7
Sam
26
71
M
4
D
40
5
5
6
Mary
32
65
F
4
D
40
6
5
6
Dawn
40
68
F
0
I
40
7
8
8
Tom
28
71
M
4
R
40
8
9
9
Terry
30
72
M
2
I
40
9
9
9
John
35
68
M
4
D
40
10
10
9
Patty
36
64
F
0
I
40
8
8
9
Chris
40
66
M
0
R
40
8
10
9
| Name | Age | Height (inches) | Gender | Years of college | Political affiliation | Hours of work per week | Satisfaction with job | Satisfaction with income | Satisfaction with economy |
| Jessica | 25 | 67 | F | 4 | R | 40 | 5 | 5 | 7 |
| Sam | 26 | 71 | M | 4 | D | 40 | 5 | 5 | 6 |
| Mary | 32 | 65 | F | 4 | D | 40 | 6 | 5 | 6 |
| Dawn | 40 | 68 | F | 0 | I | 40 | 7 | 8 | 8 |
| Tom | 28 | 71 | M | 4 | R | 40 | 8 | 9 | 9 |
| Terry | 30 | 72 | M | 2 | I | 40 | 9 | 9 | 9 |
| John | 35 | 68 | M | 4 | D | 40 | 10 | 10 | 9 |
| Patty | 36 | 64 | F | 0 | I | 40 | 8 | 8 | 9 |
| Chris | 40 | 66 | M | 0 | R | 40 | 8 | 10 | 9 |
Solution
We use a paired t test to do it because it tests the same subject twice.
Let mu_d be the mean difference between Satisfaction with job and Satisfaction with income
The test hypothesis:
Ho: mu_d =0 (i.e. null hypothesis)
Ha: mu_d not equal to 0 (i.e. alternative hypothesis)
The test statistic is
t=mean difference/(std. dev./vn)
=-0.333/(0.866/sqrt(9))
=-1.15
The degree of freedom =n-1=9-1=8
Assume that the significant level a=0.05
It is a two-tailed test.
The critical values are t(0.025, df=8)=2.31 or -2.31 (from student t table)
The rejection regions are if t<-2.31 or t>2.31, we reject the null hypothesis.
Since t=-1.15 is between -2.31 and 2.31, we do not reject the null hypothesis.
So we can not conclude that there is a difference between their satisfaction with their jobs and their satisfaction with their incomes.
If we use independent t-test, we need to test the different subjects
| 7.333 | mean Group 1 | ||
| 7.667 | mean Group 2 | ||
| -0.333 | mean difference (Group 1 - Group 2) | ||
| 0.866 | std. dev. | ||
| 0.289 | std. error | ||
| 9 | n | ||
| 8 | df |
