Question

Automobile insurance is more expensive for teenage drivers than for older drivers. To justify this cost difference, insurance companies claim that the younger drivers are much more likely to be involved in costly accidents. To test this claim, a researcher obtains information about registered drivers from the department of motor vehicles and selects a sample of n = 300 accident reports from the police department. The motor vehicle department reports the percentage of registered drivers in each age category as follows: 16% are under age 20; 28% are 20 to 29 years old; and 56% are age 30 or older. The number of accident reports for each age group is as follows.

Under Age Age 30

age 20 20-29 or older

68 92 140

Do the data indicate that the distribution of accidents for the three age groups is significantly different from the distribution of drivers? Compare these data to a "no preference" null condition. Test with = .05. (Use 2 decimal places.)

χ 2-critical =

χ 2 =

What is your decision regarding the null? Type either “reject” or “accept” in the box

Answer 1

degree of freedom =categories-1=			2
for 0.05 level and 2 df :crtiical value X2 =			5.991	from excel: chiinv(0.05,2)

applying chi square goodness of fit test:

	relative	observed	Expected	residual	Chi square
Category	frequency(p)	Oi	Ei=total*p	R2i=(Oi-Ei)/√Ei	R2i=(Oi-Ei)2/Ei
under 20	0.1600	68	48.00	2.8868	8.3333
20-29	0.2800	92	84.00	0.8729	0.7619
>30	0.5600	140	168.00	-2.1602	4.6667
total	1.00	300	300		13.7619
test statistic X2=		13.76

since test statistic falls in rejection region we reject null hypothesis