Question

Artificial trees? An association of Christmas tree growers in Indiana wants to know if there is a difference in preference for natural trees between urban and rural households. So the association sponsored a survey of Indiana households that had a Christmas tree last year to find out. In a random sample of $160$rural households, $64$had a natural tree. In a separate random sample of $261$urban households, $89$had a natural tree. A $95\%$confidence interval for the difference (Rural – Urban) in the true proportion of households in each population that had a natural tree is $-0.036\mathrm{to}0.154$. Does the confidence interval provide convincing evidence that the two population proportions are equal? Explain your answer.

Short answer

It provides convincing evidence that two population proportion are equal.

Step-by-step solution

Given Information

It is given that we have$(-0.036,0.154)$at$95\%$confidence interval.

Explanation

The interval $(-0.036,0.154)$contains zero, It is likely that difference of proportion is zero. Two population proportions can be equal.

It implies that there is possibility that population proportions are equal.

It can be concluded that there is no convincing evidence that two population proportions are not equal.