How to Calculate Confidence Interval
What is Confidence Interval?
A confidence interval (CI) gives a range of plausible values for a population parameter based on a sample. A 95% CI means: if we repeated this study many times, 95% of the resulting intervals would contain the true population value.
Step-by-Step Guide
- 1Calculate the sample mean (x̄) and standard deviation (s)
- 2Determine the z* critical value for your confidence level (95% → z* = 1.96)
- 3Calculate standard error: SE = s / √n
- 4Margin of error: ME = z* × SE
- 5CI = (x̄ − ME, x̄ + ME)
Worked Examples
Input
n=100, mean=50, SD=10, 95% CI
Result
(48.04, 51.96)
ME = 1.96 × 10/√100 = 1.96
Input
n=30, mean=75, SD=15, 99% CI
Result
(67.94, 82.06)
ME = 2.576 × 15/√30 = 7.06
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