23.23 In the courtroom. A criminal trial can be thought of as a decision problem, the two possible decisions being “guilty” and “not guilty.’’ Moreover, in a criminal trial there is a null hypothesis in the sense of an assertion that we will continue to hold until we have strong evidence against it. Criminal trials are, therefore, similar to hypothesis testing.

  1. (a) What are H0 and Ha in a criminal trial? Explain your choice of H0.

  2. (b) Describe in words the meaning of Type I error and Type II error in this setting, and display the possible outcomes in a diagram like Figure 23.3 and 23.4.

  3. (c) Suppose that you are a jury member. Having studied statistics, you think in terms of a significance level α, the (subjective) probability of a Type I error. What considerations would affect your personal choice of α? (For example, would the difference between a charge of murder and a charge of shoplifting affect your personal α?)