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 plus or minus​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?

Answer 1

No.

Explanation:

Based on the​ sample, "52% of registered voters plan on voting for Robert Smith with a margin of error of plus or minus​3%." The margin of error was based on a​ 95% confidence level.

Then 95% Confidence Interval is between 49% and 55%. Since confidence interval also includes non-majority proportions, the assumption that "95% confidence, Robert Smith will win the election" cannot be made.