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5. Suppose a drug company has 10 new drugs they are testing this year. For each drug, they will carry out a test of significance
5. Suppose a drug company has 10 new drugs they are testing this year. For each drug, they will carry out a test of significance based on a large clinical trial, comparing the drug to placebo. All the clinical trials will be conducted independently, and the drugs are unrelated to each other. Suppose that none of the drugs are really different from placebo. If the company uses a 5% threshold for p-values in all the tests, what is the chance that they will get at least one drug for which they will reject the null hypothesis and conclude that the drug is different from placebo? (Hint: For a single test, the chance of rejecting the null hypothesis even though it is true is out of 100. This means that for a single test, the chance of correctly accepting the null hypothesis is out of 100. Now use the complement rule and multiplication rule to find the chance of rejecting the null hypothesis on at least one test.)
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