Chapter 6.6, Problem 74E

The paper referenced in the previous exercise also included data for a second radiologist, Radiologist 2. Based on the data from the previous exercise for Radiologist 1 and the data in the accompanying table for Radiologist 2, write a paragraph comparing the accuracy of sex predictions made by these two radiologists.

6.85 Radiologists are often asked to predict the sex of a baby from ultrasound images made during pregnancy. The authors of the paper “The Use of Three Dimensional Ultrasound for Fetal Gender Determination in the First Trimester” (The British Journal of Radiology, [2003]: 448-451) followed up on 159 predictions made by a particular radiologist (Radiologist 1) to determine whether or not they were correct. Data from the paper is summarized in the accompanying table.

1. a. Assuming that these data are representative of sex predictions made by Radiologist 1, estimate the probability that a sex prediction is correct, given that the baby is male.
2. b. Assuming that these data are representative of sex predictions made by Radiologist 1, estimate the probability that a sex prediction is correct, given that the baby is female.
3. c. For Radiologist 1, is a sex prediction more likely to be correct if the baby is male? Explain.
4. d. Estimate the probability that a sex prediction made by Radiologist 1 is correct.