For major environmental remediation projects to be successful, they must have public support. The article "Modelling the Non-Market Environmental Costs and Benefits of Biodiversity Using Contingent Value Data" (D. Macmillan, E. Duff, and D. Elston, Environmental and Resource Economics, 2001:391-410) reported the results of a survey in which Scottish voters were asked whether they would be willing to pay additional taxes in order to restore the Affric forest. Out of 189 who responded, 61 said they would be willing to pay.
a. Assuming that the 189 voters who responded constitute a random sample, find a 90% confidence interval for the proportion of voters who would be willing to pay to restore the Affric forest.
b. How many voters should be sampled to specify the proportion to within ±0.03 with 90% confidence?
c. Another survey is planned, in which voters will be asked whether they would be willing to pay in order to restore the Strathspey forest. At this point, no estimate of this proportion is available. Find a conservative estimate of the sample size needed so that the proportion will be specified to within ±0.03 with 90% confidence?