Hypothesis testing for a proportion: Candidates A is running for office. It is claimed that the race is a dead heat, that is, that the true current proportion for the candidate is p = 0.50. A pollster polls a randomly selected group of n = 1000 people and finds that 535 prefer A (hence pˆ(n) = 0.535).

(a) At the 95% confidence level, using the null hypothesis H0 : p = 0.50 versus the alternative H1 : p ?= 0.50, would you reject the "dead heat" claim ? What is the P - value?

(b) Suppose that A believes he will be the winner, p > 0.5. At the 95% confidence level, using the null hypothesis H0 : p = 0.50 versus the alternative H1 : p > 0.50, would you reject the "dead heat" claim and conclude that A will win? What about at the 99% level?

(c) At the 95% confidence level, using the null hypothesis H0 : p = 0.50 versus the alternative H1 : p > 0.50, what is the probability of Type II error, if we use as the specific alternative hypothesis p = p1 = 0.52? What is the Power of the test?