Question

In a study of vehicle ownership, it has been found that 31% of U.S. households do not own a vehicle, with 50% owning 1 vehicle, and the remaining owning 2 or more vehicles. The data for a random sample of 199 households in a resort community are as follows:

51 owned 0 vehicles, 109 owned 1 vehicle, and the remaining owned 2 or more vehicles.

When testing (at the 5% level of significance) whether the vehicle-ownership distribution in this community differs from that of the nation as a whole what is the test statistic? (please round your answer to 3 decimal places) (Please show all work so I will know how to do this!)

Answer 1

Applying chi square goodness of fit test:

	relative	observed	Expected	residual	Chi square
category	frequency	Oi	Ei=total*p	R2i=(Oi-Ei)/√Ei	R2i=(Oi-Ei)2/Ei
No vehicle	0.310	51	61.69	-1.36	1.852
1 vehicle	0.500	109	99.50	0.95	0.907
2 or more vehicles	0.190	39	37.81	0.19	0.037
total	1.000	199	199		2.797

from above test statistic =2.797

degree of freedom =categories-1=3-1=2

(as test statistic 2.797 is less than critical value 5.991 therefore we can not reject null hypothesis)