Question 4.108

4.108 Normal approximation for a sample proportion.

A sample survey contacted an SRS of 700 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 see in the next chapter that in this situation the proportion of the sample who voted has approximately the Normal distribution with mean and standard deviation .

  1. If the respondents answer truthfully, what is ? This is the probability that the sample proportion estimates the mean of 0.56 within plus or minus 0.04.
  2. In fact, 72% of the respondents said they had voted . If respondents answer truthfully, what is ? This probability is so small that it is good evidence that some people who did not vote claimed that they did vote.