Question

3. Chi-Squared test of Independence. 

Use the sample data below to test whether car color affects the likelihood of being in an accident at 0.05 level of significance. 

Answer 1

H0: Null Hypothesis: Car color does not affect the likelihood of being in an accident

HA: Alternative Hypothesis: Car color affects the likelihood of being in an accident

Assuming H0 the Expected Frequencies are got asfollows:

	Red	Blue	Green	Total
Car has been in an accident	51X97/172=28.76	31.02	37.22	97
Car has not been in an accident	22.24	23.98	28.78	75
Total	51	55	66	172

Chi Square Table is formed as follows:

O	E	(O - E)2/E
28	28.76	0.02
33	31.02	0.13
36	37.22	0.04
23	22.24	0.03
22	23.98	0.16
30	28.78	0.05
Total = =		0.43

ndf = (c - 1) X (r - 1)

    =(3 - 1) X (2 - 1) = 2

By Technology, P - Value = 0.8071

Since P - Value = 0.8071 is greater than = 0.05, thedifference is not significant. Fail to reject null hypothesis.

Conclusion:

The data do not support the claim that car color affects the likelihood of being in an accident