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Hypothesis testing
Lesson 6 of 10
Standard practice

Significance levels and critical regions

Objective. Find a critical region and decide whether to reject H₀.

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  2. 2. Worked example
  3. 3. Practice
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Learn: 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?

n = 20
Illustrated card showing n = 20
  1. 1P(X ≥ 15) under B(20, 0.5) ≈ 0.021.
  2. 20.021 < 0.05.
  3. 3So 15 lies in the critical region.

Answer: Yes — reject H₀

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Common mistake. Using the full 5% in each tail of a two-tailed test.

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