The following table is a summary of randomly chosen student evaluations of facul
ID: 3219566 • Letter: T
Question
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
48
39
36
123
Below Average
32
31
54
117
Total
80
70
90
240
If faculty rank and evaluation are independent, how many assistant professors would have been expected to receive above average evaluations?
Find the test statistic, p-value, and critical value if significance is less than .05.
Do the data provide significant evidence at the .05 level that faculty rank and evaluation are dependent?
In analysis of variance, which of the following is true if the F statistic is zero?
Rank
Evaluation
Assistant Professor
Associate Professor
Professor
Total
Above Average
48
39
36
123
Below Average
32
31
54
117
Total
80
70
90
240
Explanation / Answer
H0: faculty rank and evaluation are independent
H1: faculty rank and evaluation are not independent
Let the los be alpha = 5%
The expected frequencies are
Chisquare contribution values are
Degrees of freedom: 2
Test Statistic, X^2: 7.5690
Critical X^2: 5.991471
P-Value: 0.0227
Here P-value < alpha 0.05, so we reject H0
Thus, we conclude that faculty rank and evaluation are not independent
i.e. there is evidence at the .05 level that faculty rank and evaluation are dependent
Rank Evaluation Assistant Associate Professor Total Above 41 35.875 46.125 123 Below 39 34.125 43.875 117 Total 80 70 90 240Related Questions
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