1. An opinion poll asked British Columbians: "Are you in favour of a Las-Vegas-style casino in Vancouver? Yes or No". A random sample of 500 British Columbians found that 130 were in favour of such a casino.
(a) Construct a 89% confidence interval estimate of the overall percentage of the B.C. population in favour of such a casino.
(b) The government also wants to estimate what percent of British Columbians favour allowing cigarette smoking in casinos. The government requires that the error on the estimate be no more than 3% with 89% confidence. What size of sample would be required to do this?
2. Peter, the head of a survey organization, is planning to do a survey to estimate the percentage of people who intend to vote for the federal Liberal Party in an upcoming by-election. He wants the estimate of the percentage to be correct to within 2%, 19 times out of 20. At first, Peter has absolutely no idea what fraction of the population will vote Liberal. However, Peter's assistant Janice believes that the Liberal Party will receive approximately 75% of the vote in that riding. If survey costs are $10 per person, how much money can be saved by using Janice's estimate of the percentage rather than Peter's estimate of "no idea"?