is there a relationship between the IQ of workers and there

is there a relationship between the IQ of workers and there job perfomance? a sample of 400 cases.

1- find the matrix of expected values

2- what test is appropriate for this problem

3-state null and alternate hypothesis

4-find test statistic

5-degree of freedom?

6-critical value?

7-p-value?

8- conclusion at alpha .10?

		poor	fair	good	total
	below average	67	64	25	156
intelligence	average	42	76	56	176
	above average	10	23	37	70
	total	119	163	118	400

Solution

Expected Frequencies

poor

fair

good

Total

below average

46.41

63.57

46.02

156

average

51.765

70.905

51.33

174

above average

20.825

28.525

20.65

70

Total

119

163

118

400

chi square test is appropriate.

3-state null and alternate hypothesis

Null hypothesis: There is no relationship between the IQ of workers and their job performance.

Alternate hypothesis: There is a relationship between the IQ of workers and their job performance.

4-find test statistic

Calculations

fo-fe

20.5900

0.4300

-21.0200

-9.7650

5.0950

4.6700

-10.8250

-5.5250

16.3500

(fo-fe)^2/fe

9.1348

0.0029

9.6011

1.8421

0.3661

0.4249

5.6269

1.0701

12.9454

Chi-Square Test Statistic

41.014

5-degree of freedom?

DF= (3-1)(3-1) =4

6-critical value?

Critical Value at 0.10 level

    7.779

7-p-value?

P= 0.0000

8- conclusion at alpha .10?

We reject at 0.10 level of significance.

We conclude that there is a relationship between the IQ of workers and their job performance

Expected Frequencies
	poor	fair	good	Total
below average	46.41	63.57	46.02	156
average	51.765	70.905	51.33	174
above average	20.825	28.525	20.65	70
Total	119	163	118	400