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A smoke alarm can be thought of as a test, with the null idea "there is no fire"…

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Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

A smoke alarm can be thought of as a test, with the null idea "there is no fire". The alarm sounds when there is no fire. Which kind of error is this? Later, a real fire starts and the alarm stays silent. Which kind of error is that? A study uses $\alpha = 0.05$ . If its null idea is true, what is the probability of a Type I error?

Need a reminder? The key ideaShow

Reject the null idea when the p-value is at most $\alpha$ . A Type I error is a false alarm and a Type II error a missed effect. Among $m$ independent tests of true null ideas, the chance of at least one false alarm is $1 - (1 - \alpha)^m$ .

The worked solution

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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.

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