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Determine the critical value for a one-mean z-test with a two-tailed test and α = 0.05.

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Final answer:

The critical values for a two-tailed z-test with α = 0.05 are approximately -1.96 and +1.96. These values are used to determine whether the null hypothesis should be rejected based on the test statistic.

Step-by-step explanation:

To determine the critical value for a one-mean z-test with a two-tailed test and α = 0.05, we look at the standard normal distribution (Z-distribution). Since the test is two-tailed, the α level is split between the two tails of the distribution, allocating 0.025 to each tail. Using the Z-table, we can find the critical z-values that correspond to the areas in the tails.

The critical z-value for the left tail, with an area of 0.025 to its left, is approximately -1.96. Similarly, for the right tail, the area of 0.025 to its right corresponds to a critical z-value of approximately +1.96. Therefore, these are the values you would compare your test statistic against to decide whether to reject the null hypothesis.

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