A paper describes a study of the use of MRI (Magnetic Resonance Imaging) exams in the diagnosis of breast cancer. The purpose of the study was to determine if MRI exams do a better job than mammograms of determining if women who have recently been diagnosed with cancer In one breast have cancer in the other breast. The study participants were 980 women who had been diagnosed with cancer in one breast and for whom a mammogram did not detect cancer in the other breast.
These women had an MRI exam of the other breast, and 131 of those exams indicated possible cancer. After undergoing biopsies, it was determined that 40 of the 131 did in fact have cancer in the other breast, whereas 91 did not. The women were all followed for one year, and two of the women for whom the MRI exam did not indicate cancer in the other breast were subsequently diagnosed with cancer that the MRI did not detect.
Suppose that for women recently diagnosed with cancer In only one breast, the MRI is used to decide between the two "hypotheses.
H0: woman has cancer in the other breast
Ha: woman does not have cancer In the other breast
(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 does have cancer in the other breast Is cancer-free. Is this a Type 1 or a Type II error?
B) There Is a second type of error that is possible In this setting. Describe this error.
A Type II error would be coming to the conclusion that the woman_cancer in the other breast when in fact she_cancer in the other breast.

Question

15-05-2020
Mathematics

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A paper describes a study of the use of MRI (Magnetic Resonance Imaging) exams in the diagnosis of breast cancer. The purpose of the study was to determine if MRI exams do a better job than mammograms of determining if women who have recently been diagnosed with cancer In one breast have cancer in the other breast. The study participants were 980 women who had been diagnosed with cancer in one breast and for whom a mammogram did not detect cancer in the other breast.
These women had an MRI exam of the other breast, and 131 of those exams indicated possible cancer. After undergoing biopsies, it was determined that 40 of the 131 did in fact have cancer in the other breast, whereas 91 did not. The women were all followed for one year, and two of the women for whom the MRI exam did not indicate cancer in the other breast were subsequently diagnosed with cancer that the MRI did not detect.
Suppose that for women recently diagnosed with cancer In only one breast, the MRI is used to decide between the two "hypotheses.
H0: woman has cancer in the other breast
Ha: woman does not have cancer In the other breast
(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 does have cancer in the other breast Is cancer-free. Is this a Type 1 or a Type II error?
B) There Is a second type of error that is possible In this setting. Describe this error.
A Type II error would be coming to the conclusion that the woman_cancer in the other breast when in fact she_cancer in the other breast.

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omololaj501 omololaj501 · Answer 1 · 2020-05-19T03:23:06+02:00

Answer:

Step-by-step explanation:

A type I error occurs when the null hypothesis is rejected in favor of the alternative hypothesis when the null hypothesis is actually true.

A type II error occurs when the researcher fails to reject the null hypothesis when the null is false.

H0: woman has cancer in the other breast

Ha: woman does not have cancer In the other breast

A) One possible error would be deciding that a woman who does have cancer in the other breast Is cancer-free. Is this a Type 1 or a Type II error?

This error is a type I error as the patient does have cancer which should warrant failing to reject the null but the null was rejected in favour of the alternative.

A Type II error would be coming to the conclusion that the woman does have cancer in the other breast when in fact she does not have cancer in the other breast.

This is a second type of error that can occur and it is a type II error: failing to reject the null when not true.