Hypothesis testing
Lesson 6 of 10
Significance levels and critical regions
Objective. Find a critical region and decide whether to reject H₀.
The key idea
The critical region holds the outcomes so unlikely under H₀ that they would make you reject it. Its total probability is at most the significance level.
Worked example
n = 20, p = 0.5, 5% one-tailed upper test. Is 15 in the critical region?
- 1P(X ≥ 15) under B(20, 0.5) ≈ 0.021.
- 20.021 < 0.05.
- 3So 15 lies in the critical region.
Answer: Yes — reject H₀
Practice
Each question comes with a picture and a listen button. Try it first, then reveal the answer.
Common mistake. Using the full 5% in each tail of a two-tailed test.
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