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ConfidLab
The range that likely contains the true population mean.
A 95% confidence interval doesn't mean there's a 95% chance the true mean is in this specific range — it means that if you repeated the sampling process many times, about 95% of the intervals you'd construct would contain the true mean.
The margin of error shrinks with the square root of sample size — quadrupling your sample size only halves the margin of error, which is why polls need surprisingly large samples to get tight intervals.
95% confidence interval
[94.632, 105.368]
Margin of error: ±5.368
What you entered
Standard error
15 ÷ √30= 2.7386Margin of error
1.96 × 2.7386= 5.3677Interval
100 ± 5.3677= [94.6323, 105.3677]Result
Interval: [94.632, 105.368]
We're 95% confident the true population mean lies between 94.632 and 105.368.