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  owners who had recently purchased an automobile.

	Education
Quality Rating	Some HS	HS Grad	Some College	College Grad
Average	30	35	20	60
Outstanding	45	45	50	95
Exceptional	25	20	30	45

a. Use a  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 -value is - Select your answer -less than .01between .01 and .025between .025 and .05between .05 and .10greater than .10Item 2

What is your conclusion?

- Select your answer -Cannot concludeConcludeItem 3 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 appearappearItem 7 to be satisfied with the recent purchase of their automobile.   of owners rated their automobile as Outstanding or Exceptional.

Answer 1

Chi-Square Test of independence
	Observed Frequencies
	0
Quality Rating	Some HS	HS Grad	Some College	College Grad			Total
Average	30	35	20	60			145
Outstanding	45	45	50	95			235
Exceptional	25	20	30	45			120
Total	100	100	100	200			500
	Expected frequency of a cell = sum of row*sum of column / total sum
	Expected Frequencies
	Some HS	HS Grad	Some College	College Grad			Total
Average	100*145/500=29	100*145/500=29	100*145/500=29	200*145/500=58			145
Outstanding	100*235/500=47	100*235/500=47	100*235/500=47	200*235/500=94			235
Exceptional	100*120/500=24	100*120/500=24	100*120/500=24	200*120/500=48			120
Total	100	100	100	200			500
	(fo-fe)^2/fe
Average	0.0345	1.2414	2.793	0.069
Outstanding	0.0851	0.0851	0.191	0.011
Exceptional	0.0417	0.6667	1.5000	0.1875

a)

Chi-Square Test Statistic,χ² = Σ(fo-fe)^2/fe =   6.91

Number of Rows =   3
Number of Columns =   4
Degrees of Freedom=(#row - 1)(#column -1) = (3- 1 ) * ( 4- 1 ) =   6
p value >0.10

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

b)

Average	145/500 = 29%
Outstanding	47%
Exceptional	24%

New owners appear to be satisfied with the recent purchase of their automobile. 71% (to whole number) of owners rated their automobile as Outstanding or Exceptional.