EXAMPLE 5 Margin of error and sample size

In Example 2, we compared the results of taking many SRSs of size n = 100 and many SRSs of size n = 1015 from the same population. We found that the variability of the middle 95% of the sample results was about three times larger for the smaller samples.

Our quick formula estimates the margin of error for SRSs of size 1015 to be about 3.1%. The margin of error for SRSs of size 100 is about

Because 1015 is roughly 10 times 100 and the square root of 10 is 3.1, the margin of error is about three times larger for samples of 100 people than for samples of 1015 people.