Question

In a recent year U.S. retail automobile sales were categorized as the chart describes. A random sample of 150 recent purchases indicated the results that are also included in the data set. At the .10 level of significance, is there sufficient evidence to conclude that the proportions of at least one type of car purchased differed from the report?

Model	frequency %	Sample Values
Luxury	15.6	25
Large	6	12
Midsize	42	60
Small	36.4	53

Answer 1

Null hypothesis:Ho: proportions of car is same as per report

Alternate hypothesis:Ha: proportions of at least one type of car purchased differed from the report

degree of freedom =categories-1=

3

for 3 df and 0.1 level of signifcance critical region       χ2=

6.251

Applying chi square test:

	relative	observed	Expected	residual	Chi square
category	frequency	Oi	Ei=total*p	R2i=(Oi-Ei)/√Ei	R2i=(Oi-Ei)2/Ei
Luxury	0.156	25	23.400	0.33	0.109
Large	0.060	12	9.000	1.00	1.000
Midsize	0.420	60	63.000	-0.38	0.143
Small	0.364	53	54.600	-0.22	0.047
total	1.000	150	150		1.299

as test statistic is less than critical value we can not reject null hypothesis

we do not have evidence to conclude that proportions of at least one type of car purchased differed from the report