The strongest risk factor for breast cancer is age; as a woman gets older, her risk of developing breast cancer increases. According to statistics from the National Cancer Institute, the average percentage of American women in their 60's who develop breast cancer is 3.56%.

Among women who have breast cancer, a mammogram provides a correct result about 85% of the time. For women who do not have breast cancer, a mammogram is correct 95% of the time.

a) Calculate the PPV of a mammogram for women in their 60's.

b) Suppose we wanted to calculate the PPV of a mammogram for an age group with a lower risk of developing cancer. Will the PPV be higher or lower than the value calculated in part a)? Explain your reasoning in language accessible to someone who has not taken a statistics class. c) Suppose that two new mammogram imaging technologies have been developed which can improve the PPV associated with mammograms; Technology A improves sensitivity to 99% (but specificity remains at 95%), while Technology B improves specificity to 99% (while sensitivity remains at 85%).

i. Which technology offers a higher increase in PPV?

ii. Explain the conceptual reasoning behind your answer in part i. You may reference the results of calculations as part of your answer; however, note that an answer consisting solely of comparing numeric results is insufficient