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In our justice system, judges instruct juries to find the defendant guilty only if there is   ...

In our justice system, judges instruct juries to find the defendant guilty only if there is    “evidence beyond a reasonable doubt”. In general, what would be the result if judges instructed juries to:

  1. compromise between Type I and Type II errors?
  2. never commit a Type I error?
  3. never commit a Type II error?
Math   Statistics-And-Probability   
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Answer #1

a) If it is instructed to compromise between type I and type II error, the result will be to declare an individual guilty only if there is enough evidence against him. Clearly the method is completely probabilistic (i.e. not deterministic). As a result some of the innocent persons may be wrongly classified as guilty and some of the guilty persons may be wrongly classified as innocent.

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b) If it is instructed not to commit a type I error, it means no guilty person would be wrongly classified as innocent assuming the person is guilty as the null belief.

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c) If it is instructed not to commit a type II error, it means no innocent person would be wrongly classified as guilty assuming the person is guilty as the null belief.

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