Question

A conglomerate of Christmas tree growers in Oregon wants to know if there is a difference in preference for live Christmas trees between urban and rural regions of the state. They randomly surveyed 160 rural households that put up a Christmas tree the previous season and found that 64 had used a live tree. In a separate random survey, 89 of 261 urban household had put up a live tree the previous season. The 95% confidence interval for the difference of the true proportion of all households (rural - urban) in Oregon that preferred a live tree is between -0.036 and 0.154. Based on the confidence interval, is there convincing evidence that the two population proportions are different

Answer 1

0 is part of the confidence interval, which means that there is not convincing evidence that the two population proportions are different.

Explanation:

Based on a confidence interval for the difference of proportions, there will be significant evidence that the proportions are different if 0 is not part of the confidence interval for the difference of proportions.

In this question:

Confidence interval between -0.036 and 0.154

0 is part of the confidence interval, which means that there is not convincing evidence that the two population proportions are different.