A survey of property owners' opinions about a street-widening project was taken to determine if owners' opinions were related to the distance between their home and the street. A randomly selected sample of 100 property owners was contacted and the results are shown next. 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 property owners' opinions about a street-widening project was taken to determine if owners' opinions were related to the distance between their home and the street. A randomly selected sample of 100 property owners was contacted and the results are shown next.  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% level of significance, we need to look at the t-distribution table with 99 degrees of freedom (100 sample size - 1). Since this is a two-tailed test, we need to split the 5% level of significance into two equal tails (2.5% each). Looking at the table, the closest value to 2.5% is 0.0250, with a corresponding t-value of 1.984. Multiplying this value by -1 gives us the lower critical value of -1.984. The upper critical value is the same in magnitude but with a positive sign (+1.984). Adding or subtracting these values from the sample mean gives us the confidence interval. Alternatively, we can use the t-test formula to calculate the test statistic and compare it to the critical value.

A Survey of Property Owners' Opinions About a Street-Widening Project