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Problem Value: 1 point(s). Problem Score: 0%. Attempts Remaining: Unlimited. (1 point) Breast cancer screening ~ Breast cancer is the most common cancer in females in the United States and throughout the world. A digital mammography test (the process of using low-energy X-rays to examine the human breast for diagnosis and screening) is one of the typical techniques for early detection of breast cancer. Suppose a digital mammography test has a sensitivity of 0.98, and a specificity of 0.705 for breast cancer detection. 1) Given a theoretical population of 10,000, assume that the base rate of this population is 0.07. Complete the table below for this scenario.. Test Positive Test Negative Total Have Breast Cancer Do not have Breast Cancer Total 10,000 2) In what proportion of cases do we expect the test will indicate the patient does not have breast cancer? 3) In what proportion of cases do we expect the test will indicate the patient has breast cancer?
4) Among the cases where the test indicates the respondent has breast cancer, in what proportion of cases should we expect the respondent to actually have the disease? 5) Among the cases where the test indicates the respondent does not have breast cancer, in what proportion of cases should we expect the respondent to actually be healthy? 6) Consider a second scenario with a base rate of 0.23, does the probability of actually having breast cancer if someone tests positive increase, decrease or remain the same? Justify your answer by filling out the below table. Test Positive Test Negative Total Have Breast Cancer Do not have Breast Cancer Total 10,000 Increase, Decrease, or Stay the Same: ?