Chapter 5: Q. 3 (page 308)

Mammograms Many women choose to have annual mammograms to screen for breast
cancer after age $40$ . A mammogram isn’t foolproof. Sometimes the test suggests that a
woman has breast cancer when she really doesn’t (a “false positive”). Other times the test
says that a woman doesn’t have breast cancer when she actually does (a “false negative”).
Suppose the false negative rate for a mammogram is $0.10 .$
a. Explain what this probability means.
b. Which is a more serious error in this case: a false positive or a false negative? Justify
your answer.

Expert verified

a) The probability of the mammogram's false-negative rate must be interpreted.

b) This probability might be interpreted as the percentage of false-negative findings in a large number of trials.

Step by step solution

We have to tell what this probability means.

The probability of the mammogram's false-negative rate must be interpreted.
In this problem, the chance of a mammography false-negative rate is given $0.10$

We have to tell which is a more serious error in this case

This probability might be interpreted as the percentage of false-negative findings in a large number of trials.
As a result, if we use mammography on a large number of women with cancer, approximate) of them will have a $0.10 %$ negative test.