Answer to Question #337236 in Statistics and Probability for Snow

Question

ACTIVITY 7. EXPLORING MORE ELEMENTS OF HYPOTHESIS TESTING

A. Complete the table showing the rejection regions for common values of 𝜶.

Alternative Hypothesis

𝜶 Left-Tailed Right-Tailed Two-Tailed 𝛼 = .10 1. ___________ z > 1.28 z < -1.645 or z > 1.645

𝛼 = .05 z < -1.645 2. _________ z < -1.96 or z > 1.96

𝛼 = 0.25 3. ___________ z > 1.96 4. _______________

𝛼 = .01 z < -2.33 5.__________ z < -2.58 or z > 2.58

Answer 1

1.

The rejection region for right-tailed test for $\alpha=0.10$ is

$$R = \{z: z > 1.28\}$$

The rejection region for two-tailed test for $\alpha=0.10$ is

$$R = \{z: z < -1.645\ or\ z>1.645\}$$

2.

The rejection region for left-tailed test for $\alpha=0.05$ is

$$R = \{z: z <-1.645\}$$

The rejection region for two-tailed test for $\alpha=0.05$ is

$$R = \{z: z < -1.96\ or\ z>1.96\}$$

3.

The rejection region for right-tailed test for $\alpha=0.025$ is

$$R = \{z: z > 1.96\}$$

4.

The rejection region for left-tailed test for $\alpha=0.01$ is

$$R = \{z: z <-2.33\}$$

5. The rejection region for two-tailed test for $\alpha=0.01$ is

$$R = \{z: z < -2.58\ or\ z>2.58\}$$