the following summary of a statistical study gives a sample statistic and a margin of error. find the confidence interval.
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 57% of the voters favor the republican candidate, with a margin of error of 4 percentage points. what is the confidence interval?
The confidence interval can be calculated by adding and subtracting the margin of error from the sample statistic.
In this case, the sample statistic is 57% and the margin of error is 4 percentage points.
To find the lower bound of the confidence interval, subtract the margin of error from the sample statistic: 57% - 4% = 53%.
To find the upper bound of the confidence interval, add the margin of error to the sample statistic: 57% + 4% = 61%.
Therefore, the confidence interval is 53% to 61%.