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The type I error is 0.0027 only when a two tailed test is used with a z-score of ±3. There are many occasions when a one-tailed test is more appropriate and with the same test would have half the Type I error.

Furthermore, it is more usual for the researcher to specify the type I error first - 0.05, 0.01 or 0.001 are favourites - and to select one-or two-tailed critical region after that. It is, therefore, more likely that the Type I error is a "round" number (5%, 1% or 0.1%) while the critical z-score is not.

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Q: Why is the type one error 0.0027?
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