Colonoscopy is a medical procedure that is designed to find and remove precancerous lesions in the colon before they become cancerous. In a sample of 51,460 people without colorectal cancer, 5043 had previously had a colonoscopy, and in a sample of 10,292 people diagnosed with colorectal cancer, 720 had previously had a colonoscopy.

a. Construct a 95% confidence interval for the difference in the proportions of people who had colonoscopies between those who were diagnosed with colorectal cancer and those who were not.

b. Does the confidence interval contradict the claim that the proportion of people who have had colonoscopies is the same among those with colorectal cancer and those without?