Type I and Type II Errors Math Example 1

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Example 1

medium
Define Type I and Type II errors. A court uses 'innocent until proven guilty.' Identify which type of error corresponds to (a) convicting an innocent person, (b) acquitting a guilty person.

Solution

  1. 1
    Type I error (false positive, α\alpha): reject H0H_0 when H0H_0 is true; probability = α\alpha
  2. 2
    Type II error (false negative, β\beta): fail to reject H0H_0 when H0H_0 is false; probability = β\beta
  3. 3
    (a) Convicting innocent: H0H_0 = innocent; rejecting H0H_0 (convicting) when person is actually innocent = Type I error
  4. 4
    (b) Acquitting guilty: H0H_0 = innocent; failing to reject H0H_0 (acquitting) when person is guilty = Type II error

Answer

(a) Convicting innocent = Type I error. (b) Acquitting guilty = Type II error.
Type I and II errors are trade-offs — reducing one typically increases the other (for fixed sample size). The legal system historically prioritizes minimizing Type I errors (wrongful conviction) by requiring 'proof beyond reasonable doubt' (very small α).

About Type I and Type II Errors

Type I error (α\alpha): rejecting H0H_0 when it is actually true (false positive). Type II error (β\beta): failing to reject H0H_0 when it is actually false (false negative).

Learn more about Type I and Type II Errors →

More Type I and Type II Errors Examples

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Example 4 hard

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