Example ① Errors in hypothesis testing:
・Type I error: rejecting H₀ when H₀ is true (α is the probability)
・Type II error: failing to reject H₀ when H₁ is true (β is the probability)
・Type I error: rejecting H₀ when H₀ is true (α is the probability)
・Type II error: failing to reject H₀ when H₁ is true (β is the probability)
Example ② What happens when the significance level is changed from 5% to 1%?
Solution:Type I errors decrease, but Type II errors increase because rejection becomes stricter.
Solution:Type I errors decrease, but Type II errors increase because rejection becomes stricter.
Key Point
- The trade-off between α and β
- Both can be reduced by increasing n
Practice Problems
- Does “we could not reject H₀” mean that “H₀ is true”?
Solutions and Explanations
- Solution:No. It only means that there is insufficient evidence; it does not actively support H₀.