Hypothesis testing for a proportion : Candidates A is running for office. It is claimed that race is a dead heat, that is, that the true current proportion for candidate is p = 0.50. A pollster polls a randomly chosen group of n = 1000 people and finds out that 535 prefer A (hence pˆ(n) = 0.535).
(a) At the 95% confidence level, using the null hypothesis H0 : p = 0.50 versus alternative H1 : p ?= 0.50, would you reject the "dead heat" claim ? Determine the P - value?
(b) Assume 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 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 alternative H1 : p > 0.50, determine the probability of Type II error, if we employ as the specific alternative hypothesis p = p1 = 0.52? What is the Power of the test?