Homework SourseThe following table is a summary of randomly chosen student
The following table is a summary of randomly chosen student evaluations of faculty at a university over a three-year period. The researcher is interested in whether the distribution of evaluations differs by faculty rank.
Rank
Evaluation
Assistant Professor
Associate Professor
Professor
Total
Above Average
44
36
34
114
Below Average
31
29
51
111
Total
75
65
85
225
Which of the following correctly characterizes the p-value?
a.
p-value < .01
b.
.01 < p-value < .025
c.
.025 < p-value < .05
d.
.05 < p-value < .10
e.
p-value > .10
Do the above data provide evidence at the .025 level that evaluation and faculty rank are dependent?
a.
yes
b.
no
c.
cannot be determined
d.
maybe?
e.
Pie
| Rank | ||||
| Evaluation | Assistant Professor | Associate Professor | Professor | Total |
| Above Average | 44 | 36 | 34 | 114 |
| Below Average | 31 | 29 | 51 | 111 |
| Total | 75 | 65 | 85 | 225 |
Solution
The following table is a summary of randomly chosen student evaluations of faculty at a university over a three-year period. The researcher is interested in whether the distribution of evaluations differs by faculty rank.
Rank
Evaluation
Assistant Professor
Associate Professor
Professor
Total
Above Average
44
36
34
114
Below Average
31
29
51
111
Total
75
65
85
225
Chi-Square Test
Observed Frequencies
Column variable
Calculations
Row variable
Assistant Professor
Associate Professor
Professor
Total
fo-fe
Above Average
44
36
34
114
6
3.0667
-9.0667
Below Average
31
29
51
111
-6
-3.0667
9.0667
Total
75
65
85
225
Expected Frequencies
Column variable
Row variable
Assistant Professor
Associate Professor
Professor
Total
(fo-fe)^2/fe
Above Average
38
32.9333
43.0667
114
0.9474
0.2856
1.9088
Below Average
37
32.0667
41.9333
111
0.9730
0.2933
1.9604
Total
75
65
85
225
Data
Level of Significance
0.025
Number of Rows
2
Number of Columns
3
Degrees of Freedom
2
Results
Critical Value
7.3778
Chi-Square Test Statistic
6.3683
p-Value
0.0414
Do not Reject the null hypothesis
Which of the following correctly characterizes the p-value?
a.
p-value < .01
b.
.01 < p-value < .025
c.
.025 < p-value < .05
d.
.05 < p-value < .10
e.
p-value > .10
Do the above data provide evidence at the .025 level that evaluation and faculty rank are dependent?
a.
yes
b.
no
c.
cannot be determined
d.
maybe?
e.
Pie
| Rank | ||||
| Evaluation | Assistant Professor | Associate Professor | Professor | Total |
| Above Average | 44 | 36 | 34 | 114 |
| Below Average | 31 | 29 | 51 | 111 |
| Total | 75 | 65 | 85 | 225 |
