pregnancy test on 100 women who are known to be pregnant, of whom 90 are positive using the test. pregnancy test on 100 other women who are known to not be pregnant, of whom 93 are negative using the test.

a. What is the observed sensitivity of the test?

b. What is the observed specificity of the test?

c. The company anticipates that of the women who will be using the pregnancy kit, 10% will actually be pregnant. Find the probability that an individual who tests positive truly is pregnant.

d. Let's assume that in the women's health clinic, the physicians are screening the subjects who are planning to get pregnant. Therefore, we would expect higher proportion of these women to get pregnant. How would this modify the probability computed in the previous section? Interpret you conclusion.

e. The researchers propose to administer two diagnostic tests simultaneously to provide more nuanced information about the pregnancy diagnosis. The second diagnostic test has a sensitivity of 0.91 and a specificity of 0.95. Assuming the two diagnostic tests are independent, and the prevalence of pregnancy is 10%, what is the probability that a woman who tests positive on the first test (with the sensitivity of 0.90 and a specificity of 0.93) also tests positive on the second test (with the sensitivity of 0.91 and a specificity of 0.95) has the disease?