Question

We want to make a comparison on the proportion of deaths due to lung cancer in the general population of chemical plant workers versus the proportion of deaths due to lung cancer for those working in a new chemical plant. We draw a sample and find the proportion of deaths due to lung cancer in the general population of chemical plant workers nationwide is estimated at 12.8% (n=250). Suppose that of 100 deaths that occurred in a new chemical plant, 22 were found to be due to lung cancer. We wish to determine whether there is a difference between the proportion of deaths from lung cancer in this plant and the proportion in the general population of chemical plant workers. The hypotheses for this test are
_{Ho: P1 P2 = 0}
vs. . And α=0.05.
What is the z-test statistic for the difference in proportions?

	A) z=0.0185
	B) z=1.98
	C) z=0.09
	D) z=2.58
	E) z=1.40

Answer 1

H0: p1 = p2

Ha: p1 $\neq$ p2

Sample proportion $\hat{p}$ 1 = 22 / 100 = 0.22

Sample proportion $\hat{p}$ 2 = 0.128

Test statistics

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

= [ 0.22 - 0.128] / sqrt [ 0.22 ( 1 - 0.22) / 100 + 0.128 ( 1 - 0.128) / 250]

= 1.98