Question:

Surveys have been widely used by politicians around the world as a way of monitoring the opinions of the electorate. Six months ago, a survey was undertaken to determine the degree of support for a national party leader. Of a sample of 1,100, 56% indicated that they would vote for this politician. This month, another survey of 800 voters revealed that 46% now support the leader.

a) At the 5% significance level, can we infer that the national leader's popularity has decreased?
b) At the 5% significance level, can we infer that the national leader's popularity has decreased by more than 5%?
c) Estimate with 95% confidence the decrease in percentage support between now and 6 months ago.