A radiologist investigates whether a new (less costly) method for identifying esophageal cancer is as effective as the gold standard. He obtains the following test results: false positive = 0, true positive = 46, false negative = 1, true negative = 17. (a) What is the sensitivity of the test? (Round your answer to four decimal places.) 0.9787 (b) Consider the following Excel spreadsheet. BINOMDIST(45, 47, p, TRUE) Р 0.8000 1.000 0.8100 0.999 0.8200 0.999 0.8300 0.998 0.8400 0.997 0.8500 0.996 0.8600 0.993 0.8700 0.988 0.8800 0.982 0.8900 0.972 0.9000 0.956 0.9100 0.933 0.9200 0.899 0.9300 0.850 0.9400 0.782 0.9500 0.688 0.9600 0.566 0.9700 0.414 0.9800 0.242 0.9900 0.080 0.9950 0.023 0.9990 0.001 0.9995 0.000 True positves True positive + False negative BINOMDIST(46, 47, p, TRUE) 1.000 1.000 1.000 1.000 1.000 1.000 0.999 0.999 0.998 0.996 0.993 0.988 0.980 0.967 0.945 0.910 0.853 0.761 0.613 0.376 0.210 0.046 0.023 46 47 46 = 46+1 = 0.9787234043 = 0.9787 Provide a 95% CI for the sensitivity. (Enter your answer using interval notation. Round your numerical values to two decimal places. Hint: The above Excel spreadsheet might be useful.) Please explain how to do the enclosed ( ) manually
A radiologist investigates whether a new (less costly) method for identifying esophageal cancer is as effective as the gold standard. He obtains the following test results: false positive = 0, true positive = 46, false negative = 1, true negative = 17. (a) What is the sensitivity of the test? (Round your answer to four decimal places.) 0.9787 (b) Consider the following Excel spreadsheet. BINOMDIST(45, 47, p, TRUE) Р 0.8000 1.000 0.8100 0.999 0.8200 0.999 0.8300 0.998 0.8400 0.997 0.8500 0.996 0.8600 0.993 0.8700 0.988 0.8800 0.982 0.8900 0.972 0.9000 0.956 0.9100 0.933 0.9200 0.899 0.9300 0.850 0.9400 0.782 0.9500 0.688 0.9600 0.566 0.9700 0.414 0.9800 0.242 0.9900 0.080 0.9950 0.023 0.9990 0.001 0.9995 0.000 True positves True positive + False negative BINOMDIST(46, 47, p, TRUE) 1.000 1.000 1.000 1.000 1.000 1.000 0.999 0.999 0.998 0.996 0.993 0.988 0.980 0.967 0.945 0.910 0.853 0.761 0.613 0.376 0.210 0.046 0.023 46 47 46 = 46+1 = 0.9787234043 = 0.9787 Provide a 95% CI for the sensitivity. (Enter your answer using interval notation. Round your numerical values to two decimal places. Hint: The above Excel spreadsheet might be useful.) Please explain how to do the enclosed ( ) manually
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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![**Radiology, Cancer**
A radiologist investigates whether a new (less costly) method for identifying esophageal cancer is as effective as the gold standard.
He obtains the following test results:
- False positive = 0
- True positive = 46
- False negative = 1
- True negative = 17
**(a) Sensitivity of the Test**
The formula for sensitivity is:
\[
\text{Sensitivity} = \frac{\text{True Positives}}{\text{True Positives} + \text{False Negatives}}
\]
Calculating the sensitivity:
\[
\text{Sensitivity} = \frac{46}{46 + 1} = 0.9787
\]
**(b) Excel Spreadsheet Analysis**
The following Excel spreadsheet provides values of the binomial distribution function for different probabilities (p):
| p | BINOMDIST(45, 47, p, TRUE) | BINOMDIST(46, 47, p, TRUE) |
|--------|--------------------------|--------------------------|
| 0.8000 | 1.000 | 1.000 |
| 0.8100 | 0.999 | 1.000 |
| 0.8200 | 0.999 | 1.000 |
| 0.8300 | 0.998 | 1.000 |
| 0.8400 | 0.997 | 1.000 |
| 0.8500 | 0.996 | 1.000 |
| 0.8600 | 0.993 | 0.999 |
| 0.8700 | 0.988 | 0.999 |
| 0.8800 | 0.982 | 0.998 |
| 0.8900 | 0.972 | 0.996 |
| 0.9000 | 0.956 | 0.993 |
| 0.9100 | 0.933 | 0.988 |
| 0.9200 | 0.899 | 0.980 |
| 0.9300 | 0.850 | 0.967 |
| 0.9400 | 0.782 | 0.945 |](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faeadb183-1175-48ee-be1d-be4cbd36e1e9%2Fda91a825-b7f6-4095-98fc-805af94b4194%2Fh6r23b_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Radiology, Cancer**
A radiologist investigates whether a new (less costly) method for identifying esophageal cancer is as effective as the gold standard.
He obtains the following test results:
- False positive = 0
- True positive = 46
- False negative = 1
- True negative = 17
**(a) Sensitivity of the Test**
The formula for sensitivity is:
\[
\text{Sensitivity} = \frac{\text{True Positives}}{\text{True Positives} + \text{False Negatives}}
\]
Calculating the sensitivity:
\[
\text{Sensitivity} = \frac{46}{46 + 1} = 0.9787
\]
**(b) Excel Spreadsheet Analysis**
The following Excel spreadsheet provides values of the binomial distribution function for different probabilities (p):
| p | BINOMDIST(45, 47, p, TRUE) | BINOMDIST(46, 47, p, TRUE) |
|--------|--------------------------|--------------------------|
| 0.8000 | 1.000 | 1.000 |
| 0.8100 | 0.999 | 1.000 |
| 0.8200 | 0.999 | 1.000 |
| 0.8300 | 0.998 | 1.000 |
| 0.8400 | 0.997 | 1.000 |
| 0.8500 | 0.996 | 1.000 |
| 0.8600 | 0.993 | 0.999 |
| 0.8700 | 0.988 | 0.999 |
| 0.8800 | 0.982 | 0.998 |
| 0.8900 | 0.972 | 0.996 |
| 0.9000 | 0.956 | 0.993 |
| 0.9100 | 0.933 | 0.988 |
| 0.9200 | 0.899 | 0.980 |
| 0.9300 | 0.850 | 0.967 |
| 0.9400 | 0.782 | 0.945 |
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