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

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