Question

days before a presidential election, a nationwide random sample of registered voters was taken. based on this random sample, it was reported that \52% of registered voters plan on voting for robert smith with a margin of error of ±3%.\ the margin of error was based on a 95% confidence level. can we say with 95% confidence that robert smith will win the election if he needs a simple majority of votes to win? choose the correct answer below. a. yes, since over 50% of the voters in the sample say they will vote for robert smith b. yes, because 50% is within the bounds of the confidence interval. c. no, because 50% is within the bounds of the confidence interval d. no, because the margin of error can never be more than 1%

Explanation:

A confidence interval gives a range of values within which the true population proportion is likely to lie. Here, the sample proportion is \(52\%\) and the margin of error is \(\pm3\%\). So the confidence interval is \(52\% - 3\%=49\%\) to \(52\%+ 3\% = 55\%\). A simple majority is \(50\%\). Since \(50\%\) is within the confidence interval \((49\%,55\%)\), we cannot be \(95\%\) confident that Robert Smith will win (because the lower bound of the confidence interval is \(49\%\) which is less than \(50\%\)).

Answer:

C. No, because \(50\%\) is within the bounds of the confidence interval.