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.

1. 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

2. 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

3. 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

4. 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

5. 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

6. 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

7. 225