Question

Explain how a court trial is like hypothesis testing. Include the steps of a hypothesis test and why a verdict is “not guilty” instead of innocent.

Answer 1

1. To prove someone is guilty, we start by assuming they are innocent.
2. We retain that hypothesis until the facts make it unlikely beyond a reasonable doubt.
3. Then, and only then, we reject the hypothesis of innocence and declare the person guilty.

Hypothesis testing is very much like a court trial.

Ho: Defendant is innocent

HA: Defendant is guilty

We then present the evidence—collect data.

Then we judge the evidence—”Could these data plausibly have happened by chance if the null hypothesis were true?”

If they were very unlikely to have occurred, then the evidence raises more than a reasonable doubt in our minds about the null hypothesis.

Example-

A man is accused of murder

Null Hypothesis: He is innocent

Evidence: Police have evidence of victim’s blood on his shirt and was caught with murder weapon in his hand

Probability that he is innocent would be very, very low

So we would reject the null hypothesis and claim the alternative hypothesis that he is guilty

If the evidence is not strong enough to reject the presumption of innocent, the jury returns with a verdict of “not guilty”

? The jury does not say that the defendant is innocent.

? All it says is that there is not enough evidence to convict, to reject innocence.

? The defendant may, in fact, be innocent, but the jury has no way to be sure.

? Said statistically, we fail to reject the null hypothesis.

? We never declare the null hypothesis to be true, because we simply do not know whether it's true or not.

? Therefore we never“accept the null hypothesis”