Question

1. Suppose that the table below displays the results of a pregnancy test administered to a sample of 150 females that are either pregnant or not pregnant. Please answer the questions that follow based on the sample taken from a population. Note that every probability is an approximation of the population probabilities.
   1. What is the prevalence of pregnancy, i.e., P(S)?
   2. What is the probability that a randomly selected individual will be pregnant, i.e., P(Preg)?
   3. What is the probability that a randomly selected individual will test positive, i.e., P(Pos)?
   4. What is the number of females in the sample with a false positive test?
   5. What is the sensitivity of this test? That is, what is P(Pos|Preg)?
   6. What is the number of females in the sample with a false negative test?
   7. What is the specificity? That is, what is P(Neg|Preg^c)?
   8. What is the positive predictive value for this test, i.e., P(S|Pos)?
   9. What does the positive predictive value of this test mean contextually?

	Pregnant	Not Pregnant	Total
Test Positive	64	6	70
Test Negative	3	77	80
Total	67	83	150

Answer 1

FORMULA OF PROBABILITY IS:

P= (NUMBER OF FAVOURABLE OUTCOME / TOTAL NUMBER OF OUTCOMES)

a) The prevalence of pregnancy i.e., P(S) is defined as the percentage of actual number of women that are pregnant and test positive to the total number of women who are pregnant that is

P(S) = (Number of women pregnant and test positive / total number of women that are pregnant)

P(S) = (64/67) = 0.95 or (95%)

b). The probability that a randomly selected individual will be pregnant, i.e., P(Preg) is the ratio of total number of women that are pregnant to the total number of women in the sample that is

P(Preg) = (Number of women that are pregnant / total number of the women)

P(Preg) = (67/150) = 0.45

c). The probability that a randomly selected individual will test positive, i.e., P(Pos) is the ratio of the total number of women that test positive to the total number of women in the sample that is

P(Pos) = (Number of women test positive / total number of women)

P(Pos) = (70/150) = 0.47

d) . The number of females in the sample with a false positive test means that the women is not pregnant but the test show the positive result. Therefore number of women corresponding to 'test positive' and 'not pregnant' in the table is 6.