Question: A sample. survey contacted an SRS 01663 registered voters in Oregon shortly after an election and asked respondents whether they had voted. Voter records show that \(56 \%\) of registered voters had actually voted. We will see in the next chapter that in this situation the proportion \(\hat{p}\) of the sample who voted has approximately the normal distribution with mean \(\mu=0.56\) and standard deviation \(\sigma=0.019\).

1. If the respondents answer truthfully, what is \(P(0.52 \leq \hat{p} \leq 0.60)\) ? This is the probability that the statistic \(\hat{p}\) estimates the parameter $0.56$ within plus or minus $0.04
2. In fact, 72% of the respondents said they had voted \((\hat{p}=0.72)\). If respondents answer truthfully, what is \(P(\hat{p} \geq 0.72)\) ? This probability is so small that it is good evidence that some people who did not vote claimed that they did vote.

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