Margin of Error and Confidence Intervals

The margin of error tells you how much the sample result might differ from the true population value. [formula] Example: If a poll finds 52% support with a margin of error of ±3%, the true support is likely between 49% and 55%. This range is called the confidence interval.

Example: A survey finds that 40% of students prefer online classes, with a margin of error of ±4%. What is the confidence interval?

Larger sample size → smaller margin of error (more precise). Higher confidence level → larger margin of error (more certain but less precise). The approximate formula (for proportions): [formula] where n is the sample size. To halve the margin of error, you need 4 times the sample size!

Example: A poll of 400 people has a margin of error of ±5%. About what margin of error would a poll of 1,600 people have?