Normal approximation for a sample proportion.

A sample survey contacted an SRS of 663 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 ˆp of the sample who voted has approximately the Normal distribution with mean μ = 0.56 and standard deviation σ = 0.019.

(a) If the respondents answer truthfully, what is P(0.52 ≤ ˆp ≤ 0.60)? This is the probability that the statistic ˆp estimates the parameter 0.56 within plus or minus 0.04.

(b) In fact, 72% of the respondents said they had voted ( ˆp = 0.72). If respondents answer truthfully, what is P( ˆp ≥ 0.72)? This probability is so small that it is good evidence that some people who did not vote claimed that they did vote.