Question

Chi Square Test of Independence A vehicle quality survey asked new owners a variety of questions about their recently purchased cars. One questions 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, college graduate, and university graduate. Assume the sample data below are for 500 owners who had recently purchased a car.

	Education
Quality Rating	Some HS	HS Grad	College Grad	University Grad
Average	35	30	20	60
Outstanding	45	45	50	90
Exceptional	20	25	30	50

a. Compute the value of x² for a test of independence.

b. Use a 0.05 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?

c. What is the p-value and what is your conclusion?

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

Answer 1

a)

Observed Frequencies
	Education
Quality Rating	Some HS	HS Grad	College Grad	University Grad	Total
Average	35	30	20	60	145
Outstanding	45	45	50	90	230
Exceptional	20	25	30	50	125
Total	100	100	100	200	500

Expected Frequencies
	Education
Quality Rating	Some HS	HS Grad	College Grad	University Grad	Total
Average	29	29	29	58	145
Outstanding	46	46	46	92	230
Exceptional	25	25	25	50	125
Total	100	100	100	200	500

(fo-fe)^2/fe
1.241379	0.034483	2.793103	0.068966
0.021739	0.021739	0.347826	0.043478
1	0	1	0

chisq = sum(Oi-Ei)^2/Ei = 6.5727

b)

ho: new owner’s vehicle quality rating is independent of the owner’s education
h1: new owner’s vehicle quality rating is independent of the owner’s education
chisq = 6.572713643
df = (R-1)*(c-1) = 6
critical value = chisq(a,df) = chisq(0.05,6) = 12.59158724
Since, chisq < chisq(a,df), i fail to reject ho and conclude that new owner’s vehicle quality rating is independent of the owner’s education

c)
p-Value   0.362173771
Since p>5%, i fail to reject ho and conclude that new owner’s vehicle quality rating is independent of the owner’s education.

d)

Quality Rating	overall %
Average	29%	145/500
Outstanding	46%	230/500
Exceptional	25%	125/500

46% of the people gave a outstanding rating ; 29% of the people give average rating; and 25% of the people give exceptional rating.

Hence I can say that new owners rate the quality of the recent car for change as mostly outstanding rating