The following table is a summary of randomly chosen student evaluations of facul
ID: 3055498 • 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
42
39
36
117
Below Average
38
31
54
123
Total
80
70
90
240
a. If faculty rank and evaluation are independent, how many assistant professors would have been expected to receive above average evaluations?
b. What's the value of the test statistic??
c. What's the critical value if the significance level is .05?
d. What's the p-value (any value in your range if you used a table)?
e. Do the data provide significant evidence at the .05 level that faculty rank and evaluation are dependent?
Rank
Evaluation
Assistant Professor
Associate Professor
Professor
Total
Above Average
42
39
36
117
Below Average
38
31
54
123
Total
80
70
90
240
Explanation / Answer
### By using R command
> Above=c(42,39,36)
> Above
[1] 42 39 36
> Below=c(38,31,54)
> Below
[1] 38 31 54
> chisq.test(Above,Below)
Pearson's Chi-squared test
data: Above and Below
X-squared = 6, df = 4, p-value = 0.1991
a) The number of assistant professors would have been expected to receive above average evaluations
= (42*117)/80
= 61.425
=61
b) Null Hypothesis: faculty rank and evaluation are independent
against
Alternative Hypothesis:faculty rank and evaluation are not independent
Test statistics: X-squared = 6
c) Chi squared critical Value is
X2(0.05,4)=11.143
d) p-value = 0.1991
E) Since P value is greater than the level of significance we are unable to reject the null hypothesis.
hence data does not provide significant evidence at the .05 level that faculty rank and evaluation are dependent.
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