Not everyone likes Luke Skywalker. Of 35 randomly chosen residents of Mos Eisley, 22 looked at Luke and said they didn't like him.

(a) Use a binomial probability approach to determine if there is evidence from our poll data the proportion of people who don't like Luke is greater than 0.5 in Mos Eisley at the level = 0.05. State your hypotheses, identify your distribution and test statistic, report your p-value (use R or an online applet), and write conclusion.

(b) Report the p-value you would get in (a) using a z-test (no need to write the additional setup-just find and report the p-value).

(c) If done correctly, these p-values should have a small amount of difference. Which of these test methods produces the "exact" p-value? Briefly explain your answer.