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pose a standard antibiotic kills a particular type of bacteria 80% of the eria. Using principles of hypothesis testing (covered in Chapter 7), rese Suppose there is a true probability (true efficacy) of 85% that the ne Excel, or R) for a group of 100 randomly simulated patients. Repeat "significantly better" than the standard antibiotic? (This percentage is 0.88 Consider the following questions. (i) Repeat the procedure in part (a) for each simulated patient, ass 0.000 (ii) Repeat the procedure in part (a) for each simulated patient, ass

pose a standard antibiotic kills a particular type of bacteria 80% of the eria. Using principles of hypothesis testing (covered in Chapter 7), rese Suppose there is a true probability (true efficacy) of 85% that the ne Excel, or R) for a group of 100 randomly simulated patients. Repeat "significantly better" than the standard antibiotic? (This percentage is 0.88 Consider the following questions. (i) Repeat the procedure in part (a) for each simulated patient, ass 0.000 (ii) Repeat the procedure in part (a) for each simulated patient, ass

MATLAB: An Introduction with Applications
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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Infectious Disease Suppose a standard antibiotic kills a particular type of bacteria 80% of the time. A new antibiotic is reputed to have better efficacy than the standard antibiotic. Researchers propose to try the new antibiotic on 100 patients infected with the bacteria. Using principles of hypothesis testing (covered in Chapter 7), researchers will deem the new antibiotic "significantly better" than the standard one if it kills the bacteria in at least 88 out of the 100 infected patients. (a) Suppose there is a true probability (true efficacy) of 85% that the new antibiotic will work for an individual patient. Perform a "simulation study" on the computer, based on random number generation (using, for example, MINITAB, Excel, or R) for a group of 100 randomly simulated patients. Repeat this exercise 20 times with separate columns for each simulated sample of 100 patients. For what percentage of the 20 samples is the new antibiotic considered "significantly better" than the standard antibiotic? (This percentage is referred to as the statistical power of the experiment.) X 0.88 (b) Consider the following questions. (i) Repeat the procedure in part (a) for each simulated patient, assuming the true efficacy of the new antibiotic is 80% and compute the statistical power. 0.000 (ii) Repeat the procedure in part (a) for each simulated patient, assuming the true efficacy of the new antibiotic is 90% and compute the statistical power. 0.999 ✓ (iii) Repeat the procedure in part (a) for each simulated patient, assuming the true efficacy of the new antibiotic is 95% and compute the statistical power. 1.000 (c) Plot the statistical power versus the true efficacy. Do you think 100 patients is a sufficiently large sample to discover whether the new drug is "significantly better" if the true efficacy of the drug is 95%? Why or why not? When the true efficacy of the drug is 95% a sample size of 100 results in a power greater than or equal to 0.8 x which suggests 100 patients is a large enough sample to to discover when the new drug is "significantly better." ✓
Transcribed Image Text:Infectious Disease Suppose a standard antibiotic kills a particular type of bacteria 80% of the time. A new antibiotic is reputed to have better efficacy than the standard antibiotic. Researchers propose to try the new antibiotic on 100 patients infected with the bacteria. Using principles of hypothesis testing (covered in Chapter 7), researchers will deem the new antibiotic "significantly better" than the standard one if it kills the bacteria in at least 88 out of the 100 infected patients. (a) Suppose there is a true probability (true efficacy) of 85% that the new antibiotic will work for an individual patient. Perform a "simulation study" on the computer, based on random number generation (using, for example, MINITAB, Excel, or R) for a group of 100 randomly simulated patients. Repeat this exercise 20 times with separate columns for each simulated sample of 100 patients. For what percentage of the 20 samples is the new antibiotic considered "significantly better" than the standard antibiotic? (This percentage is referred to as the statistical power of the experiment.) X 0.88 (b) Consider the following questions. (i) Repeat the procedure in part (a) for each simulated patient, assuming the true efficacy of the new antibiotic is 80% and compute the statistical power. 0.000 (ii) Repeat the procedure in part (a) for each simulated patient, assuming the true efficacy of the new antibiotic is 90% and compute the statistical power. 0.999 ✓ (iii) Repeat the procedure in part (a) for each simulated patient, assuming the true efficacy of the new antibiotic is 95% and compute the statistical power. 1.000 (c) Plot the statistical power versus the true efficacy. Do you think 100 patients is a sufficiently large sample to discover whether the new drug is "significantly better" if the true efficacy of the drug is 95%? Why or why not? When the true efficacy of the drug is 95% a sample size of 100 results in a power greater than or equal to 0.8 x which suggests 100 patients is a large enough sample to to discover when the new drug is "significantly better." ✓
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