Question

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. A test of the claim that the proportion of people who have had colonoscopies is the same among those with colorectal cancer and those without will be performed, using significance level 0.01, by answering the questions below.

a) What are the observational units?

b) What is the response variable here?

c) Describe the group variable.

d) Find the proportion within each group that had a colonoscopy.

e) Find the overall proportion of individuals across both groups that had a colonoscopy.

f) What are the appropriate null and alternative hypothesis for testing the claim?

g) Calculate the test statistics, showing your work.

h) What is the p-value for the test?

i) What is your decision based on the p-value? Please be clear in stating the decision rule and making the comparison between the p-value and the significance level.

j) State your conclusion in the context of the problem.

Answer 1

1.) The data represents cancer prevention, the observational unit is here is the data that was collected so people without colorectal cancer where we had to find who likely will have colonoscopy

2.) The response variable here is the risk of having a colorectal cancer for people who have has colonoscopy

3.) THE GROUP VARIABLE IS HERE THE GROUP of people without colorectal cancer

4.) The proportion of having colonscopy is for the group  5043/51460 = 0.09799844539

5.) All the calculation are done on minitab and hereby attached with an image

no.of people = 51460,sample size = 10292,people who had colonscopy = 5043,sample of people who had colonscopy = 720

0.022 to 0.033 output 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

It is less than significant level of 0.01 so we will reject the null and accept the alternative hypothesisi