How do we control the probability of a type I error in a hypothesis test?

Posted: September 8th, 2022

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Understanding hypothesis tests can be difficult. The important thing to keep in mind is that the purpose of a hypothesis test is to say something about an entire population based on only a sample from the population. There is always the possibility that you can reach a wrong conclusion. Actually, there are two ways you can be wrong with a hypothesis test.
The first way is to reject a true null hypothesis. In this case, that means rejecting a null hypothesis that is really true. In other words–you shut down and recalibrate a machine that is really working correctly. This is called a Type I error.
The second way you can go wrong is to fail to reject a false null hypothesis. In this case, the machine needs to be calculated but your test concludes everything is okay. So you would keep producing bags of seed that are less than advertised, maybe leading to lawsuits or a bad reputation for your brand. This is called a Type II error.
How do we control the probability of a type I error in a hypothesis test?

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