City leaders want to estimate the proportion of voters in Sheboygan Wisconsin who are in favor of
Question:
City leaders want to estimate the proportion of voters in Sheboygan Wisconsin who are in favor of a new proposition to add a bright green paint color to bike lanes in downtown areas. They take a random sample of voters and obtain a 95% confidence interval of (0.65, 0.85).
City leaders also want to pass a proposal to build a new set of public basketball courts and would like to pursue an aggressive local marketing campaign in support of the basketball courts before the upcoming community vote. The green paint in the bike lanes is a bigger priority though, and city leaders would have to divert funds from the bike lane proposal. They would feel OK with diverting these funds if they were 95% confident that over three quarters of the voters in Sheboygan are already in favor of the bike lane proposal. Based on our confidence interval above, should leaders divert funds into the basketball court marketing campaign?