1. Quebec is a large province in eastern Canada and is the only province whose residents primarily speak French. The debate about whether the province should succeed from Canada and create their own county has ebbed and flowed over the years. In a recent survey of 3,600 Quebec residents, 26% said that Quebec should separate from Canada. In the same survey, 79% agreed that Quebec society is unique from the rest of Canada.
2. Find the 90% confidence interval for the proportion of residents that would like to form their own country.
3. What does that tell us about the status of the debate?
4. Find the 90% interval for the proportion of residents that believe that Quebec has a distinct society.
5. What that tell us about the status of the debate?
6. Overall, what does the two confidence intervals tell us about the status of the debate?
7. If you increased the confidence level to 95%, would the length of the interval increase or decrease? Explain.
8. The researchers surveyed 3,600 Quebecers. What could the researchers do to shorten the length of confidence interval without changing the confidence level? Explain.
9. If the researchers wanted to reduce the margin of error by half, how many people would they need to survey? Would that be realistic? Why or why not?