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. The Excel Online file below contains the sample data for 500 owners who had recently purchased an automobile. Construct a spreadsheet to answer the following questions.
Observed Frequency Table
Education | |||||
Quality Rating | Some HS | HSGrad | SomeCollege | CollegeGrad | Total |
Average | 23 | 21 | 31 | 60 | 135 |
Outstanding | 52 | 50 | 45 | 88 | 235 |
Exceptional | 25 | 29 | 24 | 52 | 130 |
Total | 100 | 100 | 100 | 200 | 500 |
Expected Frequency Table
Education | |||||
Quality Rating | SomeHS | HSGrad | SomeCollege | CollegeGrade | Total |
Average | 27 | 27 | 27 | 81 | |
Outstanding | 47 | 47 | 94 | ||
Exceptional | 26 | 26 | 52 | ||
Total | 100 | 100 | 27 | 0 | 227 |
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 ????? (to 4 decimals).
What is your conclusion?
Cannot 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: 27% (to whole number)
Outstanding: 47% (to whole number)
Exceptional: 26% (to whole number)
New owners appear to be satisfied with the recent purchase of their automobile. 73% (to whole number) of owners rated their automobile as Outstanding or Exceptional.