Question

A poll is conducted the day before a state election for Senator. There are only two candidates running for this office. The poll results show that 59​% of the voters favor the Republican​ candidate, with a margin of error of 4 percentage points. Should the Republican expect to​ win? Why or why​ not? Choose the correct answer below.

Answer 1

The lower limit of the confidence interval is 55%, which is above 50%, so the Republican should expect to win.

Explanation:

A confidence interval of proportions has two bounds, a lower bound and an upper bound.

These bounds depend on the sample proportion and the margin of error.

The lower bound is the sample proportion subtracted by the margin of error.

The upper bound is the margin of error added to the sample proportion.

In this problem, we have that:

Sample proportion 59%

Margin of error 4%

59 - 4 = 55%

59 + 4 = 63%

The lower limit of the confidence interval is 55%, which is above 50%, so the Republican should expect to win.