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A researcher tests 40 different foods to see whether any of them is linked to better sleep…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A researcher tests different foods to see whether any of them is linked to better sleep. She uses for each test. In fact, none of the foods has any effect, and the tests are independent. Find the expected number of foods that will look significant. Find the probability that at least one will, to four decimal places.
Need a reminder? The key ideaShow
Reject the null idea when the p-value is at most . A Type I error is a false alarm and a Type II error a missed effect. Among independent tests of true null ideas, the chance of at least one false alarm is .
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Step 1. foods.
Step 2. .
Answer: foods expected, and a probability of about .
What it means. A headline about "the food that helps you sleep" from such a study is very likely a false alarm. An honest report would list all tests.
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