In the 2005 federal election, 39.62% of the electorate voted for the party A, 30.63% for the party B, and 18.91% for the Party C.
(a) A recent poll of 1000 respondents found 32.1% would support the federal party C and 26.2% would support the party A. Test whether this is sufficient evidence to show that the party A vote has dropped by more than 10% from their share of the popular vote in 2005. Use the .01 level of significance and show your manual calculations.
(b) Suppose that, in a random sample of 17 voters, only 2 indicated a preference for the party As. Test whether this is sufficient evidence to indicate that the level of support for the party As among these 17 voters is lower than the 39.62% share of the popular vote in 2005. Use the .01 level of significance and explain how you would calculate the p-value for this test. Why does this not allow us to infer anything about the national level of support for the party A's?