In a two-tailed hypothesis about a population mean with a sample size of 100 and α = 0.05, the rejection region would be ___. A)z 1.64 B)z 1.96 C)z 1.96 D)z 1.64 E)z 2.33

Question

In a two-tailed hypothesis about a population mean with a sample size of 100 and α = 0.05, the rejection region would be ___. A)z > 1.64 B)z > 1.96 C)z < -1.96 and z > 1.96 D)z < -1.64 and z > 1.64 E)z < -2.33 and z > 2.33

Quizplus · Accepted Answer

For a two-tailed hypothesis at α = 0.05 level of significance, the rejection region lies in the two extreme tails of the standard normal distribution. Each of the two tails is equal to (1 - 0.05)/2 = 0.025. Since the sample size is large (n ≥ 30), we can use the z-score test statistic.

The standard normal distribution table shows that the z-score for the upper 0.025 tail is 1.96, and the z-score for the lower 0.025 tail is -1.96. Therefore, the rejection region for a two-tailed test at α = 0.05 level of significance with a sample size of 100 is z < -1.96 or z > 1.96, which is equivalent to choice C.

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