Question

A trucking company wants to find out if their drivers are still alert after driving long hours, So, they give a test for alertness to two groups of drivers. They give the test to 330 drivers who have just finished driving 4 hours or less and they give the test to 215 drivers who have just finished driving 8 hours or more. The results of the tests are given below. Passed Failed Drove 4 hours or less 250 80 Drove 8 hours or more 140 75 Is there is a relationship between hours of driving and alertness? (Do a test for independence.) Test at the 1% level of significance. BIVA-AI E331x , - VCT 12pt Paragraph

Answer 1

Hypothesis:

H0: Variables are independent (No association)

Ha: Variables are not independent (Association)

Test:

Observed(O)	Passed	Failed	Total
Drove 4 hours or less	250	80	330
Drove 8 hours or more	140	75	215
Total	390	155	545
Expected ( E)	Passed	Failed	Total	Rtotal*Ctotal/Grand total
Drove 4 hours or less	236.1468	93.85321101	330
Drove 8 hours or more	153.8532	61.14678899	215
Total	390	155	545
	Passed	Failed	Total	(O-E)^2/E
Drove 4 hours or less	0.812679	2.044804362	2.857483
Drove 8 hours or more	1.247367	3.138536928	4.385904
Total		X^2	7.243387	SUM((O-E)^2/E)
		df	1	(r-1)*(c-1)
		P value	0.007116	Use X^2 table

X^2 stat = 7.2434

P value = 0.0071

Deciaion:

P value < 0.01, Reject H0

Conclusion:

There is enough evidence to conclude that there is a relationship between hours of driving and alertness