The paper ?Breast MRI as an Adjunct to Mammography for Breast Cancer Screening in High- Risk Patients? (American Journal of Roentgenology [2015]: 889?897) describes a study that investigated the usefulness of MRI (magnetic resonance imaging) to diagnose breast cancer. MRI exams from 650 women were reviewed. Of the 650 women, 13 had breast cancer, and the MRI exam detected breast cancer in 12 of these women. Of the 637 women who did not have breast cancer, the MRI correctly identified that no cancer was present for 547 of them. The accompanying table summarizes this information.?

Suppose that an MRI exam is used to decide between the two hypotheses

H₀: A woman does not have breast cancer

H_a: A woman has breast cancer

(Although these are not hypotheses about a population characteristic, this exercise illustrates the definitions of Type I and Type II errors.)

a. One possible error would be deciding that a woman who has breast cancer is cancer-free. Is this a Type I error or a Type II error? Use the information in the table to approximate the probability of this type of error.

b. There is a second type of error that is possible in this context. Describe this error and use the information in the table to approximate the probability of this type of error.

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Breast Cancer Breast Cancer Present Not Present Total MRI Indicated Breast Cancer 90 12 102 MRI Did Not 547 548 Indicate Breast Cancer Total 13 637 650