Suppose a study investigated the relationship between the use of oral contraceptives and development of endometrial cancer. The researchers found out that of 358 endometrial cancer patients, 18 had used the oral contraceptive (OC) Oracon at some time in their lives.
a) Find a 95% confidence interval for the prevalence of OC Oracon use among endometrial cancer patients.
b) Suppose it is known that the prevalence of OC Oracon use in the general population is 4%. Based on the CI you calculated in (a), would you say that the prevalence of OC Oracon uses among endometrial cancer patients differ from that of the general population? Justify your answer briefly.
c) Carry out a test of hypothesis to answer the question in (b). Use α=5%.
d) What is the critical value for this test at the significance level of 0.01? State your conclusion based on this critical value. Implement the test again using STATA. Are the two conclusions consistent?