Question

A Christmas tree survey was conducted to determine there was a difference between urban rural tree users in terms of artificial tree use. The results are presented in the table below. What is the 90% CI for the difference between the proportions (urban minus rural) of artificial tree users?

Total Tree Users Number with Artificial Trees 89 64 261 160 Urban Rural

	a.	(-0.211, 0.129)
	b.	(0.023, 0.441)
	c.	(-0.139, 0.021)
	d.	(-0.246, 0.234)

Answer 1

Sample proportion $\hat{p}$ 1 = 89 / 261 = 0.341

Sample proportion $\hat{p}$ 2 = 64 / 160 = 0.400

90% confidence interval for p1 - p2 is

( $\hat{p}$ 1 - $\hat{p}$ 2) - 1.945 * sqrt[ $\hat{p}$ 1 ( 1 - $\hat{p}$ 1) / n1 + $\hat{p}$ 2 ( 1 - $\hat{p}$ 2) / n2 ) ] < p1 - p2 <

( $\hat{p}$ 1 - $\hat{p}$ 2) + 1.945 * sqrt[ $\hat{p}$ 1 ( 1 - $\hat{p}$ 1) / n1 + $\hat{p}$ 2 ( 1 - $\hat{p}$ 2) / n2 ) ]

(0.341 - 0.4) - 1.645 * sqrt [ 0.341 * 0.659 / 261 + 0.4 * 0.6 / 160 ] < p1 - p2 <

(0.341 - 0.4) + 1.645 * sqrt [ 0.341 * 0.659 / 261 + 0.4 * 0.6 / 160 ]

-0.139 < p1 - p2 < 0.021

90% CI is ( -0.139 , 0.021 )