Question

(4 pts) Among drivers who have had a car crash in the last year, 230 were randomly selected and categorized by age, with the results listed in the table below. Age Dri Under 25 25-4445-64 Over 64 vers 88 57 32 53 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 χ 2- The critical value isχ The conclusion is A. There is not sufficient evidence to warrant the rejection of the claim that the distribution of crashes conforms to the distibuion of O B. There is sufficient evidence to warrant the rejection of the claim that the distribution of crashes conforms to the distibuion of ages

Answer 1

Total number of samples = n = 230

Expected frequencies are,

i) 230 * 0.16 = 36.8

ii) 230 * 0.44 = 101.2

iii) 230 * 0.27 = 62.1

iv) 230 * 0.13 = 29.9

The test statistic is,

$\chi^2 = \frac {(88 - 36.8)^2 }{36.8} +\frac {(57 - 101.2)^2 }{101.2} +\frac {(32 - 62.1)^2}{62.1} + \frac {(53 - 29.9)^2}{29.9}$

$=> \chi^2 = 122.9755$

Degrees of freedom = 4 - 1 = 3

The critical value at 0.025 significance level with df = 3 is,

$=> \chi_{crit}^2 = 9.348$

Since, $=> \chi^2 = 122.9755 > 9.348$

We conclude that, there is sufficient evidence to warrant the rejection o the claim that the distribution of crashes conforms to the distribution of ages.