Cost of environmental restoration: In a survey of 189 Scottish voters, 61 said they would be willing to pay additional taxes in order to restore the Affric forest.

a. Assuming that the 189 voters who responded constitute a random sample, construct a 99% confidence interval for the proportion of voters who would be willing to pay to restore the Affric forest.

b. Use the results from the sample of size 189 to estimate the sample size needed so that the 99% confidence interval will have a margin of error of 0.03.

c. Another survey is planned, in which voters will be asked whether they would be willing to pay in order to restore the Strathsprey forest. At this point, no estimate of this proportion is available.

Find an estimate of the sample size needed so that the margin of error of a 99% confidence interval will be 0.03.

Source: Environmental and Resource Economics 18:391–410