During the campaign for the June 1997 federal election, many opinion polls were conducted. Early in the campaign, a poll found that 47.6% of voters supported the Liberals. Then in May 1997 an Angus Reid poll found that of 3208 voters surveyed, 42% supported the Liberals (based on a report conducted for the CTV television network and the Southam newspaper chain). Some analysts suggested that this difference was within the margin of error for the polls.
a. Assuming that 3100 voters participated in the earlier poll, test the claim that there was no change in support for the Liberals between the two polls. Based on the result, did the Liberals need to change campaign strategies?
b. Construct a 95% confidence interval for the difference between the proportions of voters who supported the Liberals in the earlier poll and those who supported the Liberals in the May poll.