6) The sensitivity of a medical test is defined as the probability that the test will be positive, given that the person has the disease. The specificity of a test is defined as the probability that the test will be negative, given that the person does not have the disease.  The sensitivity for breast cancer of a mammography is approximately 79.6%. The specificity of a mammography exam is approximately 90.2% Approximately 2.4% of women under the age of 50 have breast cancer.  (a) Draw a tree diagram that represents the above data for breast cancer and mammography exams. (b) Given that a women under the age of 50 tests positive for breast cancer during a mammography exam, find the probability that she has cancer.

To diagnose colorectal cancer, the hemoccult test is conducted to detect occult blood in the stool. For symptom-free people over 50 years old who participate in screening using the hemoccult test, the following information is available. The probability that one of these people has colorectal cancer is 0.3 percent. If a person has colorectal cancer, the probability is 50 percent that he will have a positive hemoccult test. If a person does not have colorectal cancer, the probability is 3 percent that he will still have a positive hemoccult test. Imagine a person (over age 50, no symptoms) who has a positive hemoccult test in your screening. Your assignment is to use this hemoccult test scenario as an example to communicate the nature of a medical test to a lay person. (Think of a family member or a friend who is not familiar with statistics.) You need to incorporate three elements in your essay: Identify the base rate (or prevalence in medical literature), sensitivity (the…

To diagnose colorectal cancer, the hemoccult test is conducted to detect occult blood in the stool. For symptom-free people over 50 years old who participate in screening using the hemoccult test, the following information is available. The probability that one of these people has colorectal cancer is 0.3 percent. If a person has colorectal cancer, the probability is 50 percent that he will have a positive hemoccult test. If a person does not have colorectal cancer, the probability is 3 percent that he will still have a positive hemoccult test. Imagine a person (over age 50, no symptoms) who has a positive hemoccult test in your screening. What is the probability that this person actually has colorectal cancer?”

The table below shows the results of a survey about a junk food tax.     Support Oppose Unsure Male 184 363 16 Female 291 358 28   A person is selected at random from the sample.  What is the probability that a person opposes the tax or is female? Your answer should be a decimal (not a percent) correct to three decimal places.