Question

An article titled “Hypertension Drug Linked to Cancer, studies several types of high-blood-pressure drugs and links to cancer. For one type, called calcium-channel blockers, 27 out of 202 elderly patients taking the drug developed cancer. For another type, called beta-blockers, 28 out of 424 other elderly patients developed cancer. At the 1% significance level, do the data provide sufficient evidence to conclude that the probability of getting cancer higher of taking calcium-channel blockers than of taking beta-blockers.

Answer 1

p1cap = X1/N1 = 27/202 = 0.1337
p1cap = X2/N2 = 28/424 = 0.066
pcap = (X1 + X2)/(N1 + N2) = (27+28)/(202+424) = 0.0879

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

Test statistic
z = (p1cap - p2cap)/sqrt(pcap * (1-pcap) * (1/N1 + 1/N2))
z = (0.1337-0.066)/sqrt(0.0879*(1-0.0879)*(1/202 + 1/424))
z = 2.8

P-value Approach
P-value = 0.0026
As P-value < 0.01, reject the null hypothesis.

There is sufficient evidence to conclude that the probability of getting cancer higher of taking calcium-channel blockers than of taking beta-blockers.