Question

Exercise 5. In the past decade, intensive antismoking campaigns have been sponsored by both federal and private agencies. Suppose the American Cancer Society randomly sampled 1500 adults in 2000 and then 1750 adults in 2010 to determine whether there was evidence that the percentage of smokers had decreased. 555 of the surveyed adults in 2000 and 578 of the surveyed adults in 2010 were smokers. Do these data indicate that the fraction of smokers decreased over this 10- year period? Use ? = .05

Answer 1

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

p1cap = X1/N1 = 555/1500 = 0.37
p1cap = X2/N2 = 578/1750 = 0.3303
pcap = (X1 + X2)/(N1 + N2) = (555+578)/(1500+1750) = 0.3486

Test statistic
z = (p1cap - p2cap)/sqrt(pcap * (1-pcap) * (1/N1 + 1/N2))
z = (0.37-0.3303)/sqrt(0.3486*(1-0.3486)*(1/1500 + 1/1750))
z = 2.37

P-value Approach
P-value = 0.9911
As P-value >= 0.05, fail to reject null hypothesis.