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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鈥檛 foolproof. Sometimes the test suggests that a

woman has breast cancer when she really doesn鈥檛 (a 鈥渇alse positive鈥�). Other times the test

says that a woman doesn鈥檛 have breast cancer when she actually does (a 鈥渇alse negative鈥�).

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.

Short 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

01

Part (a) Step 1: Given information

We have to tell what this probability means.

02

Part (a) Step 2: Explanation

  • The probability of the mammogram's false-negative rate must be interpreted.
  • In this problem, the chance of a mammography false-negative rate is given0.10
03

Part (b) Step 1: Given information

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

04

Part (b) Step 2: Explanation

  • 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 a0.10% negative test.

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