A survey of the opinions of property owners about a street widening project was taken to determine whether the resulting opinion was related to the distance of front footage. A randomly selected sample of 100 property owners was contacted and the results are shown below. What is the critical value at the 5% level of significance?
A) 7.779
B) 9.488
C) 9.236
D) 11.070

Question

A survey of the opinions of property owners about a street widening project was taken to determine whether the resulting opinion was related to the distance of front footage. A randomly selected sample of 100 property owners was contacted and the results are shown below.  What is the critical value at the 5% level of significance?
A) 7.779 
B) 9.488 
C) 9.236 
D) 11.070

Quizplus · Accepted Answer

The critical value can be found using a chi-squared distribution table with (r-1)(c-1) degrees of freedom, where r is the number of rows (distance categories) and c is the number of columns (opinions). In this case, there are 4 distance categories and 3 opinions, so (4-1)(3-1) = 6 degrees of freedom. At a 5% level of significance, the critical value is 9.488. This is the closest value to the calculated chi-squared value in the table (9.141), which is between the values for 5% and 1%. Therefore, we choose B as the best answer.

A Survey of the Opinions of Property Owners About a Street