An opinion poll is taken on the eve of a presidential election in a large democratic country. 1600 registered voters are asked whom they would vote for in the election on the next day. Among those in the sample, 750 say they would vote for the conservative candidate and 850 say they would vote for the liberal candidate. Construct a 95% and a 99% confidence interval for the proportion of all registered voters who would vote for the liberal candidate, assuming that voters' preferences will not change between the time the poll is taken and the election day.