Question

A Clinician concerned about the population decided to do study on whether taking a low-dose aspirin reduces the chance of developing colon cancer. As part of the study, 1,000 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 were assigned to the control group that took a placebo each day. At the end of the six years, 18 of the 500 people who took the low-dose aspirin had developed colon cancer and 25 of the 500 people who took the placebo had developed colon cancer. At the significance level ?? = 0.05, do the data provide convincing statistical evidence that taking a low-dose aspirin each day would reduce the chance of developing colon cancer among all people similar to the volunteers?

(a) Define the parameters of interest and state the null and alternative hypotheses.

b) Write out the formula for the test statistic with the appropriate values substituted. Note that you do not need to calculate the final answer.

(c) If the p-value is 0.1376, write a conclusion for this hypothesis test.

Answer 1

A)

Null hypothesis Ho : P1-P2 = 0

Alternate hypothesis Ha : P1-P2 < 0

P1 = proportion of those who took low dose aspirin

P2 = proportion of those who took the placebo

B)

Test statistics = (p1-p2)/standard error

Standard error = √{P*(1-P)}*√{(1/n1)+(1/n2)}

P1 = 18/500, P2= 25/500

N1 = N2 = 500

P = pooled proportion = (18+25)/(500+500)

C)

When the P-Value is greater than the given significance level we fail to rejection Ho

Here p-value = 0.1376 > 0.05 (given significance)

We fail to reject Ho that p1-p2 = 0

So, we do not have enough evidence to conclude that taking a low-dose aspirin each day would reduce the chance of developing colon cancer among all people similar to the volunteers.