A candidate, who is running for a state senate seat, had a 47% popularity. Her campaign released a new set of ads targeting young voters. The candidate wants to know if her recent ads have improved...

A candidate, who is running for a state senate seat, had a 47% popularity. Her campaign released a new set of ads targeting young voters. The candidate wants to know if her recent ads have improved her popularity. She asks for a survey of 400 voters to answer this question. She is particularly interested in determining if her popularity is increased by 2%. find a sample size that provides an 89.5% to 90.5% chance of detecting a 2% increase in the candidate's popularity, What sample size do you propose the candidate to use for her survey?