A colonoscopy is a screening test for colon cancer, recommended as a routine test for adults over age 50. The proportion of people with colon polyps who are expected to die from colon cancer is 0.01. As a part of a study of the effectiveness of colonoscopies, a sample of 2602 people who had polyps removed during a colonoscopy were followed for 20 years, and only 12 of them died from colon cancer.

a. What proportion of the people in the sample who had polyps removed during colonoscopies eventually died from colon cancer? Is this less than the expected proportion (without colonoscopy) of 0.01?

b. Do the data provide strong evidence that the proportion of people who die from colon cancer after having polyps removed during a colonoscopy is significantly less than the expected proportion of 0.01? Carry out a test of hypothesis, completing all four steps. Be sure to clearly stale your conclusion to the research question in context. Compute the p-value in two different ways. using the binomial distribution and using the normal approximation to the binomial with continuity correction. How do the two probabilities compare in this case?

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Population proportion p 0 001 n 2602 Number of people died x 12 a Sample proport... View the full answer