The campaign manager for a political candidate claims that 55% of registered voters favor the candidate over her strongest opponent. Assuming that this claim is true, what is the probability that in a simple random sample of 300 voters, at least 60% would favor the candidate over her strongest opponent?For the situation described in Exercise 8.42, suppose that only 49% of the registered voters in the sample favor the candidate over her strongest opponent. Given this result:
a. If the campaign manager's claim is correct, what is the probability that the sample proportion would be no more than 0.49 for a sample of this size?
b. Based on your answer to part (a), speculate on whether the campaign manager's claim might be mistaken.