Wiki Page, Math 13 - Perez Sandbox : Module 23 - Estimating a Population Mean (3a of 3)

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2026-01-17T21:15:40-08:00

Let’s quickly review how the precision of a confidence interval relates to the margin of error:

An interval gives a more precise estimate when the interval is narrower. In other words, the margin of error is smaller.

An interval gives a less precise estimate when the interval is wider. In other words, the margin of error is larger.

We know that a higher confidence level gives a larger margin of error, so confidence level is also related to precision.

Increasing the confidence in our estimate makes the confidence interval wider and therefore less precise.

Decreasing the confidence in our estimate makes the confidence interval narrower, and therefore more precise.

Confidence interval estimates are useful when they have the right balance of confidence and precision. Typical confidence levels used in practice are 90%, 95%, and 99%. When we need to be really sure about our estimates, such as in life-and-death situations, we choose a 99% confidence level. So if nothing else changes, we settle for less precise estimates when we need a high level of confidence.

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