Question

According to a report by the American Cancer Society, more men than women smoke and twice as many smokers die prematurely than nonsmokers. In random samples of 200 males and 200 females, 62 of the males and 54 of the females were smokers.

• Is there sufficient evidence to conclude that the proportion of males who smoke is greater than the proportion of females who smoke? α = .01

• Calculate the p-value associated with the test

Answer 1

p1cap = X1/N1 = 62/200 = 0.31
p1cap = X2/N2 = 54/200 = 0.27
pcap = (X1 + X2)/(N1 + N2) = (62+54)/(200+200) = 0.29

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: p1 = p2
Alternate Hypothesis, Ha: p1 > p2

Rejection Region
This is right tailed test, for α = 0.01
Critical value of z is 2.33.
Hence reject H0 if z > 2.33

Test statistic
z = (p1cap - p2cap)/sqrt(pcap * (1-pcap) * (1/N1 + 1/N2))
z = (0.31-0.27)/sqrt(0.29*(1-0.29)*(1/200 + 1/200))
z = 0.88

fail to reject null hypothesis.

P-value Approach
P-value = 0.1894