A state representative is reported as saying that about 10 %...

A state representative is reported as saying that about $10 \%$ of reported auto thefts involve owners whose cars have not really been stolen, but who are trying to defraud their insurance company. What null and alternative hypotheses would be appropriate in evaluating the statement made by this legislator?

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Key Concepts

Alternative Hypothesis

The alternative hypothesis is a statement that contradicts the null hypothesis and is accepted if there is sufficient evidence against the null. In evaluating the legislator’s claim, the alternative hypothesis would specify that the true proportion of fraudulent auto theft reports is different from 10% (p ? 0.10), indicating that the actual rate of fraud might be either higher or lower than the claimed value.

One-Sample Proportion Test

This type of hypothesis test is used when making inferences about a population proportion based on a sample. It involves comparing the observed sample proportion to a hypothesized population proportion (in this case, 10%) to determine if there is a statistically significant difference. Such tests typically use a binomial distribution approximated by a normal distribution when sample sizes are large enough.

Null Hypothesis

The null hypothesis is the default position in hypothesis testing that asserts there is no change or effect—in this context, it assumes that the true proportion of fraudulent auto theft reports is exactly 10%. This hypothesis is usually stated as equality (p = 0.10) and serves as the starting point for testing any deviation from this assumed value.

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