Question

Question 12 10 pts A medical study was conducted to investigate whether taking a low- dose aspirin reduces the chance of developing colon cancer. As part of the study, 1000 adult volunteers were randomly assigned to one of two groups. Half of the volunteers were assigned to the experimental group that took a low-dose aspirin each day, and the other half was assigned to the control group that took a placebo each day. At the end of six years, 15 of the people who took the aspirin had developed colon cancer and 26 of the people who took the placebo had developed colon cancer. At the 5% level of significance, test whether taking the low-dose aspirin daily reduces the chance of developing colon cancer for all people similar to the volunteers in the study. Show all details of the test. (10 pts) HTML Editora BI y A - A - IX E53 1 - V GOVO1

Answer 1

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

p1cap = X1/N1 = 15/500 = 0.03
p1cap = X2/N2 = 26/500 = 0.052
pcap = (X1 + X2)/(N1 + N2) = (15+26)/(500+500) = 0.041

Test statistic
z = (p1cap - p2cap)/sqrt(pcap * (1-pcap) * (1/N1 + 1/N2))
z = (0.03-0.052)/sqrt(0.041*(1-0.041)*(1/500 + 1/500))
z = -1.75

P-value Approach
P-value = 0.0401
As P-value < 0.05, reject the null hypothesis.