Statistics Help?

Question

A man is on trial accused of murder in the first degree. The prosecutor presents evidence that he hopes will convince the jury to reject the hypothesis that the man is innocent. This situation can be modeled as a significance test with the following hypotheses:

Ho: The defendant is innocent

H1: The defendant is not innocent

Suppose that the null hypothesis is rejected and alternate hypothesis is accepted. Discuss the conclusion as a Type I error, a Type II error, or a correct decision, if in fact the defendant is innocent

Answer 1

First you need the definitions of a type I and type II errors.

A type one error exists when your reject the null but shouldn't have.  In this case you pronounce the man guilty when really he was innocent. The p-value gives you the probability of committing a type I error.

A type II error exists when you fail to reject the null but you should have rejected it.  Using the example above this would mean that you pronounce the defendent Not Guilty when in fact he really did commit the murder.