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In a two-tailed hypothesis about a population mean with a sample size of 100, where σ is known and α = 0.10, the rejection region would be:

A. \( z < -1.64 \) and \( z > 1.64 \)
B. \( z > 1.64 \)
C. \( z > 1.28 \)
D. \( z < -2.33 \) and \( z > 2.33 \)
E. \( z < -1.28 \) and \( z > 1.28 \)

Answer :

The rejection region is z < -1.64 and z > 1.64.

The correct option is A.

In this case, α = 0.10, which means we need to allocate 0.10/2 = 0.05 to each tail of the distribution.

Now, the z-value for the upper tail is 1.645 and the z-value for the lower tail is -1.645.

Therefore, the rejection region would be z < -1.645 and z > 1.645.

Thus, the rejection region is z < -1.64 and z > 1.64.

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Answer:

z < -1.64 and z > 1.64

Step-by-step explanation:

See section 9.2 Testing Hypotheses about a Population Mean using the z Statistic

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