# Suppose there is a true probability (true efficacy) of 85% that the new antibiotic will work for an individual patient.

## Question:

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.) Compare results for different students in the class.

**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.

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