One of the closest states in the polls for the presidential election as I write this exam is Iowa ...

One of the closest states in the polls for the presidential election as I write this exam is Iowa. Looking at the data there, the most recent poll had Clinton is at 39%, Trump at 43%, and Johnson and others for the remaining 18%. To simplify this a little bit, let’s suppose that Johnson/other is definitely correct at 18%. Thus, to win the state over Clinton, Trump would need more than 41% of the vote, since 82% remains after the Johnson/other portion is removed. 

(a) Using the poll referenced above as data, test the claim that more than 41% of likely voters will vote for Trump, under the (not necessarily true, but we’re doing basic stats here!) assumption that the above poll is a good sample of size 642. Use alpha = 0.05. (State your hypotheses, clearly show your decision process, and state your conclusion in words.)

(b) [5 points] Now suppose that the true percentage of likely voters for Trump is greater than 41%. Based on your answer to the first part of this question, which of the following is true?

(i) Your hypothesis test resulted in a Type I error

(ii) Your hypothesis test resulted in a Type II error

(iii) Your hypothesis test did not result in either a Type I or Type II error.