In a two-tailed hypothesis about a population mean with a sample size of 100 and alpha = 0.10, the rejection region would be ___. A)z 1.64 B)z 1.28 C)z 1.28 D)z 1.645 E)z 2.33

Question

In a two-tailed hypothesis about a population mean with a sample size of 100 and alpha = 0.10, the rejection region would be ___. A)z > 1.64 B)z > 1.28 C)z < -1.28 and z > 1.28 D)z < -1.645 and z > 1.645 E)z < -2.33 and z > 2.33

Quizplus · Accepted Answer

For a two-tailed hypothesis test with alpha = 0.10, we would split the alpha level into two equal tails of 0.05 each. Using a z-table, we can find the z-score cutoffs for each tail:

- The right tail cutoff is z = 1.645, which includes 0.05 of the area under the normal distribution curve to the right of that value.
- The left tail also has an area of 0.05, so we find the z-score that corresponds to the area of 0.05 to the left of that value. This is -1.645.

The rejection region, then, is defined by the values of z that fall beyond these cutoffs in both tails: z < -1.645 and z > 1.645.

In a Two-Tailed Hypothesis About a Population Mean with a Sample