Question

In: Statistics and Probability

A vehicle quality survey asked new owners a variety of questions about their recently purchased automobile....

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.

Solutions

Expert Solution

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.


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