For each hypothesis test, please clearly state your null and alternative hypotheses, test, decision, and conclusion. All tests are at the 0.05 level unless otherwise specified.
A 55-year-old Kansas woman recently received her annual mammogram, and the results of this screening test indicated the presence of breast cancer. The radiologist reading the film has a sensitivity rate for screening mammography of 85% and a specificity rate of 97%. If 1 in 1,000 women (ages 55 and older) have breast cancer, what is the probability that this 55-year-old Kansas woman has cancer given the result of her mammogram?
Hint: sensitivity = P(mammogram indicates the presence of cancer | woman has cancer); specificity = P(mammogram indicates no cancer present | woman does not have cancer); so, using Bayes' Theorem, find the positive predictive value = P(a woman has cancer | mammogram indicates the presence of cancer)
In a medical study that compared subjects with non-acute appendicitis and with acute appendicitis in terms of whether they suffered severe right abdominal pain. Such severe pain was reported by 5 of the 15 non-acute cases and by 1 of the 16 acute cases. The doctors believed that a greater density of nerve fibers in the non-acute cases could increase the chance of such pain. Conduct an appropriate test and interpret your results. In addition, calculate a relevant statistic and confidence interval.