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

To find the critical value at the 5% significance level for this survey, we need to determine the degrees of freedom (df). The df for this survey is (n-1) = (100-1) = 99. Using a t-distribution table or calculator, we can find the critical value where the area to the right is 0.05 with 99 degrees of freedom, which is 1.984. We then multiply this by the standard error of the mean to get the critical value for the distance of front footage. Using the formula for the standard error of the mean (s/√n), where s is the sample standard deviation and n is the sample size, we get: 
s = 19.12 
√n = √100 = 10 
s/√n = 1.912 
Multiplying this by 1.984 gives us the critical value of 3.795, which we then double to get the critical value for the distance of front footage. Therefore, the critical value at the 5% level of significance is 2*3.795 = 7.59, which is closest to option B, 9.488.

A Survey of the Opinions of Property Owners About a Street