Question

In the U.S. legal system, a defendant is presumed innocent until proven guilty. Consider a null hypothesis, H0, that a defendant is innocent, and an alternative hypothesis, H1, that a defendant is guilty. A jury has two possible decisions: Convict the defendant (i.e., reject the null hypothesis) or do not convict the defendant (i.e., do not reject the null hypothesis). Explain the meaning of the following for this example in the context of this example: A. A Type I error? (Do not use/state “H0,” “H1,” or formulas.) B. A Type II error? (Do not use/state “H0,” “H1,” or formulas.) C. Power (the statistical definition of Power)? (Do not use/state “H0,” “H1,” or formulas.) D. Confidence (the statistical definition of Confidence)? (Do not use/state “H0,” “H1,” or formulas.)

Answer 1

A.

Type I error is rejection of H0 given that H0 is true.

Thus, Type I error is to convict the defendant when the defendant is innocent.

B.

Type II error is fail to reject H0 given that H0 is false.

Thus, Type II error is do not convict the defendant when the defendant is guilty.

C.

Power is rejection of H0 given that H0 is false.

Thus, Type I error is convict the defendant when defendant is guilty.

D.

Confidence is fail to reject H0 given that H0 is true.

Thus, Confidence is do not convict the defendant when the defendant is innocent.