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. If the computed chi-square is 8.5, what is your decision at the 10% level of significance? A) Reject H₀; opinion and property front-footage are related. B) Accept H₀; opinion and property front-footage are related. C) Reject H₀; opinion and property front-footage are not related. D) Accept H₀; opinion and property front-footage are not related.

Question

Quizplus · Accepted Answer

We use the chi-square goodness of fit test to determine whether opinion and property front footage are related. The null hypothesis is that the two variables are independent, and the alternative hypothesis is that they are dependent. At the 10% level of significance, the critical value of chi-square with (5-1)(2-1) = 4 degrees of freedom is 9.488. Since the computed chi-square of 8.5 is less than the critical value, we fail to reject the null hypothesis. Therefore, there is not enough evidence to conclude that opinion and property front footage are related. However, we need to be cautious because our decision may be affected by the sample size, and the power of the test may be low.

A Survey of the Opinions of Property Owners About a Street