The magnitude of z for a two-tailed hypothesis test of a population mean is greater than it would be in a one-tail hypothesis test given the same level of significance.

Question

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In a two-tailed hypothesis test, the critical region is split between the two tails of the distribution, requiring a larger z-value to reach the same level of significance as compared to a one-tailed test, where the entire critical region is in one tail.

The Magnitude of Z for a Two-Tailed Hypothesis Test of a Population