Question

A researcher for an automobile manufacturer wants to see if the ages of automobiles are equally distributed among three categories: less than 3 years old, 3 to 7 years old, and 8 years old or older. A sample of 30 adult automobile owners is selected, and the results are shown. At ? = 0.05 can it be considered that the ages of the automobiles are equally distributed among 3 categories?

Category	Less Than 3 Years	3 to 7 Years	8 Years and Older
Number	8	10	12

Answer 1

here null hypothesis:Ho: ages of the automobiles are equally distributed among 3 categories

alternate hypothesis:Ha: ages of the automobiles are not equally distributed among 3 categories

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

for 2 degree of freedom and 0.05 level rejection region >5.991

applying chi square goodness of fit test:

		observed	Expected		Chi square
category	Probability(p)	Oi	Ei=total*p		R2i=(Oi-Ei)2/Ei
<3	1/3	8.000	10.000		0.4000
3-7	1/3	10.000	10.000		0.0000
>=8	1/3	12.000	10.000		0.4000
total	1.000	30	30		0.8000

here as test statistic 0.800 false below rejection region we can not reject null hypothesis

we do not have sufficient evidence to conclude that  ages of the automobiles are not equally distributed among 3 categories