In: Statistics and Probability
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.
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.