Question

Among drivers who have had a car crash in the last year, 130 were randomly selected and categorized by age, with the results listed in the table below. Age Under 25 25-44 45-64 Over 64 Drivers

Age	Under 25	25-44	45-64	Over 64
Drivers	52	31	17	30

If all ages have the same crash rate, we would expect (because of the age distribution of licensed drivers) the given categories to have 16%, 44%, 27%, 13% of the subjects, respectively. At the 0.025 significance level, test the claim that the distribution of crashes conforms to the distribution of ages

The test statistic is

χ2=

The p-value is

The conclusion is A. There is sufficient evidence to warrant the rejection of the claim that the distribution of crashes conforms to the distibuion of ages.

B. There is not sufficient evidence to warrant the rejection of the claim that the distribution of crashes conforms to the distibuion of ages.

Answer 1

Claim: The distribution of crashes conforms to the distribution of ages.

The null and alternative hypothesis is

H0: The distribution of crashes not conforms to the distribution of ages.

H1: The distribution of crashes conforms to the distribution of ages.

Level of significance = 0.025

Test statistic is

O: Observed frequency
E: Expected frequency.

E = n*pi

n = 130

	O	pi	E	(O-E)	(O-E)^2	(O-E)^2/E
	52	0.16	20.8	31.2	973.44	46.8
	31	0.44	57.2	-26.2	686.44	12.0006993
	17	0.27	35.1	-18.1	327.61	9.33361823
	30	0.13	16.9	13.1	171.61	10.1544379
Total	130					78.289

Degrees of freedom = Number of E's - 1 = 4 - 1 = 3

P-value = P( ) = 0.0000

P-value < 0.025 we reject null hypothesis.

Conclusion:

The distribution of crashes conforms to the distribution of ages.

B. There is not sufficient evidence to warrant the rejection of the claim that the distribution of crashes conforms to the distribution of ages.