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	44	39	36	119
Below Average	36	31	54	121
Total	80	70	90	240

14. If faculty rank and evaluation are independent, how many assistant professors would have been expected to receive above average evaluations?

15. What's the value of the test statistic?

16. What's the critical value if the significance level is .05?

17. What's the p-value (any value in your range if you used a table)?

18. Do the data provide significant evidence at the .05 level that faculty rank and evaluation are dependent? Yes or no?

Answer 1

14)

expected assistant professors to receive above average evaluation =row total*column total/grand total=119*80/240=39.667

15)

applying chi square test:

Ei=row total*column total/grand total	Assistant	Associate	Professor	Total
above	39.667	34.71	44.63	119
below	40.33	35.29	45.38	121
total	80	70	90	240
=(Oi-Ei)2/Ei	Assistant	Associate	Professor	Total
above	0.4734	0.5307	1.6670	2.671
below	0.4656	0.5219	1.6395	2.627
total	0.939	1.053	3.306	5.298

test statistic X² =5.298

c)

critical value if the significance level is .05 =5.991

d)

0.05 < p-value    <0.10

e)

No ; as p value is nt less than 0.05 level