A colonoscopy is a screening test for colon cancer, recommended as a routine test for adults over age 50. A new study provides the best evidence yet that this test saves lives. The proportion of people with colon polyps expected to die from colon cancer is 0.01. A sample of 2602 people who had polyps removed during a colonoscopy were followed for 20 years, and 12 of them died from colon cancer. Does this provide evidence that the proportion of people who die from colon cancer after having polyps removed in a colonoscopy is significantly less than the expected proportion (without a colonoscopy) of 0.01?

(a) What are the null and alternative hypotheses?
(b) What is the sample proportion?
(c) Figure 4.19 shows a randomization distribution for this test. Use the fact that there are 1000 dots in the distribution to find the p-value. Explain your reasoning.

(d) Does the p-value appear to show significant evidence that colonoscopies save lives?

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