Introduction To Statistics And Data Analysis
6th Edition
ISBN: 9781337793612
Author: PECK, Roxy.
Publisher: Cengage Learning,
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Chapter 10.2, Problem 13E
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
Ha: 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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The paper "Breast MRI as an Adjunct to Mammography for Breast Cancer Screening in High-Risk Patients" 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.
†
Breast CancerPresent
Breast CancerNot Present
Total
MRI IndicatedBreast Cancer
12
90
102
MRI Did NotIndicate Breast Cancer
1
547
548
Total
13
637
650
a.
Use the information in the table to approximate the probability of this type of error. (Hint: See Example 10.8. Enter your probability as a decimal)
b.
Use the information in the table to approximate the probability of this type of error. (Enter your probability as a decimal )
The paper "Breast MRI as an Adjunct to Mammography for Breast Cancer Screening in High-Risk Patients" 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.
Breast CancerPresent
Breast CancerNot Present
Total
MRI IndicatedBreast Cancer
12
90
102
MRI Did NotIndicate Breast Cancer
1
547
548
Total
13
637
650
Suppose that an MRI exam is used to decide between the two hypotheses.
H0: A woman does not have breast cancer.
Ha: 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…
Colonoscopy is a medical procedure that is designed to find and remove precancerous lesions in the colon before they become cancerous. The article “Association of Colonoscopy and Death from Colorectal Cancer” (N. Baxter, M. Goldwasser, et al., Annals of Internal Medicine, 2009:1–8) reports that in a sample of 10,292 people diagnosed with colorectal cancer, 7.0% had previously had a colonoscopy, and in a sample of 51,460 people without colorectal cancer, 9.8% had previously had a colonoscopy. Can you conclude that the percentage of people who have had colonoscopies is greater in those without colorectal cancer?
Chapter 10 Solutions
Introduction To Statistics And Data Analysis
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