Surveys have been widely used by politicians around the world as a way of monitoring the opinions of the electorate. Nine months ago, a survey was undertaken to determine the degree of support for a Democratic Party politican. Of a sample of 1100, 56% indicated that they would vote for this politician. This month, another survey was undertaken to determine the degree of support for the same Democratic Party politican. Of a sample of 800, 46% indicated they would vote for this politician.

Based on the above information,

(a) can we infer at the 5% significance level that the politician's popularity has decreased by more than 6%? Show all the necessary steps. (5 marks)

(b) compute the p-value for the test statistic. (1 mark)