Problem 5. The strongest risk factor for breast cancer is age; as a woman gets older, her risk of developing breast cancer increases. The following table shows the average percentage of American women in each age group who develop breast cancer, according to statistics from the National Cancer Institute. For example, approximately 3.56% of women in their 60's get breast cancer. Table 1: Prevalence of Breast Cancer by Age Group Age Group ' Prevalence 30 40 0.0044 40 50 0.0147 50 60 0.0238 60 70 0.0356 70 80 0.0382 A mammogram typically identies a breast cancer about 85% of the time, and is correct 95% of the time when a woman does not have breast cancer. a) Using whatever methods you wish, calculate the PPV for each age group; show your work. Describe the trend in PPV values as prevalence changes and explain the reasoning behind the relationship between prevalence and PPV. b) Suppose that two new mammogram imaging technologies have been developed which can improve the PPV associated with mammograms; one improves sensitivity to 99% (but speci city remains at 95%), while the other improves specicity to 99% (While sensitivity remains at 85%). Which technology offers a higher increase in PPV? Explain your