A recent poll of 1,423 randomly sampled likely voters shows your favorite candidate ahead, with 51.93% in favor. There are two candidates. Use hypothesis testing to infer to the larger group of all likely voters to see whether or not this indicates that your candidate is ahead in the larger population. 

a. Carefully identify the two-sided hypotheses. 

b. Perform the hypothesis test at level 0.05 and give the result. 

c. Make a careful, exact statement summarizing the result of the test and what it means. 

d. Repeat parts b and c assuming that the percentage is 56.64% instead of 51.93%. 

e. Explain why a one-sided test would be inappropriate here by showing that each of the three possible outcomes of a two-sided test would be of interest.