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Data Analysis with R - Second Edition by Tony Fischetti

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One and two-tailed tests

You may reject the null hypothesis if the test statistic falls within a region under the curve of the sampling distribution that covers 5% of the area (if the alpha level is .05). This is called the critical region. Do you remember, in the last chapter, we constructed 95% confidence intervals that covered 95% percent of the sampling distribution? Well, the 5% critical region is like the opposite of this. Recall that, in order to make a symmetric 95% of the area under the curve, we had to start at the .025 quantile and end at the .975 quantile, leaving 2.5% percent on the left tail and 2.5% of the right tail uncovered.

Similarly, in order for the critical region of a hypothesis test to cover 5% of the most extreme ...

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