Answer to Question #250760 in Statistics and Probability for Millicent

Question

Which of the options is the rejection region for testing H0: μ = 100 vs. H1: μ ¹ 100, at the 0.05 level of significance?Select one:

a. | z | < 0.95

b. | z | > 1.96

c. z > 1.65

d. z < 2.33

Answer 1

The following null and alternative hypotheses need to be tested:

$H_0:\mu=100$

$H_1:\mu\not=100$

This corresponds to a two-tailed test, for which a z-test for one mean, with known population standard deviation will be used.

Based on the information provided, the significance level is $\alpha = 0.05,$ and the critical value for a two-tailed test is $z_c = 1.96.$

The rejection region for this two-tailed test is $R = \{z: |z| > 1.96\}.$

b. $| z | >1.96$