Question

1. Questions 14 through 18 refer to the following:

   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

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

1 points

Question 15

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

1 points

Question 16

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

1 points

Question 17

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

1 points

Question 18

1. Do the data provide significant evidence at the .05 level that faculty rank and evaluation are dependent?

   		yes
   		no
   		socks
   		light bulb

Answer 1

14:

The required expected value is

15:

Here we need to use chi square test. Following is the output of chi square test:

Chi-square Contingency Table Test for Independence
			Assistant Professor	Associate Professor	Professor	Total
	Above Average	Observed	44	39	36	119
		Expected	39.67	34.71	44.63	119.00
	Below Average	Observed	36	31	54	121
		Expected	40.33	35.29	45.38	121.00
	Total	Observed	80	70	90	240
		Expected	80.00	70.00	90.00	240.00
			5.30	chi-square
			2	df
			.0707	p-value

The test statistics is

16:

Degree of freedom: df =( number of rows -1)*(number of columns-1) = (2-1)*(3-1)=2

The critical value of test statistics using excel function "=CHIINV(0.05,2)" is 5.991

17:

The p-value using excel function "=CHIDIST(5.3,2)" is: 0.0707

18:

Since p-value is greater than 0.05 so we cannot conclude that  the data provide significant evidence at the .05 level that faculty rank and evaluation are dependent.