Question

A vehicle quality survey asked new owners a variety of questions about their recently purchased automobile. One question asked for the owner’s rating of the vehicle using categorical responses of average, outstanding, and exceptional. Another question asked for the owner’s education level with the categorical responses some high school, high school graduate, some college, and college graduate. Assume the sample data below are for 500 owners who had recently purchased an automobile.

	Education
Quality Rating	Some HS	HS Grad	Some College	College Grad
Average	35	30	20	55
Outstanding	45	45	50	90
Exceptional	20	25	30	55

a. Use a .05 level of significance and a test of independence to determine if a new owner's vehicle quality rating is independent of the owner's education.

Compute the value of the test statistic (to 2 decimals).

The p-value is - Select your answer -less than .01 or between .01 and .025 or between .025 and .05 or between .05 and .10 or greater than .10

What is your conclusion?

- Select your answer -Cannot conclude or Conclude that the quality rating is not independent of the education of the owner.

b. Use the overall percentage of average, outstanding, and exceptional ratings to comment upon how new owners rate the quality of their recently purchased automobiles.

Average %
Outstanding %
Exceptional %

New owners - Select your answer -do not appear or appear to be satisfied with the recent purchase of their automobile. What percent of owners rated their automobile as Outstanding or Exceptional.

Answer 1

a)

Applying chi square test of independence:

Expected	Ei=row total*column total/grand total	Some HS	HS grad	Some college	College grad	Total
	average	28.00	28.00	28.00	56.00	140
	outstanding	46.00	46.00	46.00	92.00	230
	exceptional	26.00	26.00	26.00	52.00	130
	total	100	100	100	200	500
chi square    χ2	=(Oi-Ei)2/Ei	Some HS	HS grad	Some college	College grad	Total
	average	1.750	0.143	2.286	0.018	4.1964
	outstanding	0.022	0.022	0.348	0.043	0.4348
	exceptional	1.385	0.038	0.615	0.173	2.2115
	total	3.1564	0.2031	3.2489	0.2344	6.843
test statistic X2 =		6.84

p value =

0.336   or greater than .10

Cannot conclude that the quality rating is not independent of the education of the owner.

b)

average	28.0%
outstanding	46.0%
exceptional	26.0%

New owners appear to be satisfied with the recent purchase of their automobile. 72% of owners rated their automobile as Outstanding or Exceptional.