The rejection region changes according to the form of the alternative hypothesis.
- Two-tailed test: H₁：μ ≠ μ₀. α/2 in each tail. At 5%, reject when |Z|>1.96
- One-tailed test: H₁：μ > μ₀. All α in one tail. At 5%, reject when Z>1.65
Example ① We want to show that “the mean is greater than μ₀.” Which test should we use?
Solution:A one-tailed (upper-tailed) test.
Solution:A one-tailed (upper-tailed) test.
Key Point
- Choose a two-tailed or one-tailed test according to the direction of the claim
Practice Problems
- Find the rejection region for a 5% two-tailed test.
Solutions and Explanations
- Solution:|Z| > 1.96