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Relationship among p-value, significance level, and critical

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What is the relationship among p-value, significance level, and critical value?

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This 450 word solution discusses the relationship among p-value, significance level, and critical value.

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First a little background on hypothesis tests

When we do a hypothesis test, we first state a null and alternative hypothesis. We then calculate a test statistic that has a known probability distribution if the null hypothesis is true (this is often called the "null distribution". We can think of the test statistic as a randomly selected observation from the null distribution.

If the null hypothesis is true, we therefore expect the value of the test statistic to be a value that is a typical value of the null distribution (not a value very far in one of the tails of the distribution). If the alternative hypothesis is true, we expect to see ...

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