Confidence Interval Math Example 3

Follow the full solution, then compare it with the other examples linked below.

Example 3

easy
A 95% CI for a population mean is (42,58)(42, 58). Find the sample mean xห‰\bar{x} and the margin of error EE.

Solution

  1. 1
    Sample mean = midpoint of CI: xห‰=42+582=50\bar{x} = \frac{42 + 58}{2} = 50
  2. 2
    Margin of error = half-width: E=58โˆ’422=8E = \frac{58 - 42}{2} = 8

Answer

xห‰=50\bar{x} = 50; E=8E = 8.
Confidence intervals are symmetric around the sample mean. The midpoint gives the point estimate; half the total width gives the margin of error. You can always recover both from the endpoints of any symmetric confidence interval.

About Confidence Interval

A range of values, computed from sample data, that is likely to contain the true population parameter with a specified level of confidence.

Learn more about Confidence Interval โ†’

More Confidence Interval Examples

Example 1 medium

A sample of [formula] has [formula] and [formula]. Construct a 95% confidence interval for the popul

Example 2 hard

Compare 90% and 99% confidence intervals for [formula], [formula], [formula]. Calculate both and exp

Example 4 hard

To achieve a margin of error of [formula] with 95% confidence, given [formula], find the required sa

โ† All Confidence Interval Examples Confidence Interval Concept