Question

Among drivers who have had a car crash in the last year, 250 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	98	56	38	58

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=χ2=

Answer 1

Chi square formula
$\chi ^{2}=\sum \frac{(Oi-Ei)^{2}}{Ei}$

=143.51

k=4

Degree of freedom = k - 1 = 4 - 1 = 3

P value is = 0 (Approximately) .........................by using Excel command =CHIDIST(143.51,3)

P value is = 0 < 0.025

Therefore, we reject H0 at the 0.025 significance level.

Oi	pi	Ei=N*pi	$\frac{(Oi-Ei)^{2}}{Ei}$
98	0.16	40	84.1
56	0.44	110	26.50909091
38	0.27	67.5	12.89259259
58	0.13	32.5	20.00769231
			$\chi ^{2}=\sum \frac{(Oi-Ei)^{2}}{Ei}=143.51$