Ipsos-Reid asked 900 Canadian adults whether they approve of using illegal or unauthorized online methods to access online music. In their responses, 12% of men said they completely approve, whereas the corresponding percentage for women was 6%.

a) Construct a 90% confidence interval for the percentage of Canadian adult men who completely approve of using illegal or unauthorized online methods to access online music and interpret what this interval means. State your assumptions clearly and check the conditions.

b) Are you 99% confident that there is a difference between men and women on this issue? Suppose Ipsos-Reid had interviewed 2000 Canadian adults. How much narrower would the confidence interval in (a) be? Give your answer as a percentage of the answer in (a).

c) The population of Ontario is 10 times as large as the population of Manitoba. Should we survey 10 times as many people in Ontario as in Manitoba in order for the confidence intervals on our results to be of similar width in the two provinces?