When considering the Justice System example associated with significance testing

if the jury renders a “Not Guilty” verdict when, in-fact, the defendant was actually not innocent, then this would be a_________.

Question

When considering the Justice System example associated with significance testing

if the jury renders a “Not Guilty” verdict when, in-fact, the defendant was actually not innocent, then this would be a_________.

BlackTom AI · Accepted Answer

The question describes a courtroom scenario in the context of significance testing concepts.
First, identify the underlying hypotheses: the null hypothesis is typically that the defendant is not guilty (innocent) and the alternative is that the defendant is guilty. If the jury renders a 'Not Guilty' verdict while the defendant is actually not innocent (i.e., guilty), the decision made was to fail to reject a false null hypothesis.
Option analysis:
- Type II Error: This is the error that occurs when we fail to reject a false null hypothesis. Here, the null hypothesis (innocent) is false because the defendant is actually guilty, yet the verdict does not convict. This matches the description given in the question, so this option aligns with the concept of a Type II error.
- Type I Error (not present in the provided options, but worth noting): This would be rejecting a true null hypothesis (convicting an innocent person). That would be the opposite scenario and does not fit the described outcome.
- Any alternative phrasing that suggests correct rejection of a true state would be a Type I error, not what happened here.
- If there were options emphasizing accuracy or no error, those would be incorrect because the scenario explicitly involves an incorrect trial outcome, not a correct verdict.

In summary, the situation—Not Guilty given actual guilt—corresponds to a Type II error, since a false null hypothesis (innocence) was not rejected.

STAT 1450.02 SP2025 (28132) Checkpoint 18.5

When considering the Justice System example associated with significance testing if the jury renders a “Not Guilty” verdict when, in-fact, the defendant was actually not innocent, then this would be a_________.

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