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95% Confidence Interval Formula:
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A 95% confidence interval (CI) is a range of values that you can be 95% certain contains the true mean of the population. It provides an estimate of the precision of your sample mean and accounts for sampling variability.
The calculator uses the standard formula for 95% confidence interval:
Where:
Explanation: The margin of error (1.96 × SD/√n) accounts for both the variability in the data (SD) and the sample size (n). Larger samples and less variability produce narrower confidence intervals.
Details: Confidence intervals provide more information than just a point estimate (like the mean). They show the range of plausible values for the population parameter and indicate the precision of the estimate.
Tips: Enter the sample mean, standard deviation, and sample size. All values must be valid (n > 0, SD ≥ 0). The calculator will output the lower and upper bounds of the 95% confidence interval.
Q1: Why 95% confidence?
A: 95% is a commonly used confidence level that provides a good balance between precision and certainty. Other levels (90%, 99%) can be used depending on the context.
Q2: What does 95% confidence mean?
A: If you repeated your study many times, 95% of the calculated confidence intervals would contain the true population mean.
Q3: When is this formula appropriate?
A: For normally distributed data with known standard deviation, or when sample size is large enough (n > 30) for the Central Limit Theorem to apply.
Q4: What if my data isn't normally distributed?
A: For small samples of non-normal data, consider non-parametric methods or transformations. For large samples (n > 30), this method is generally robust.
Q5: How does sample size affect the CI?
A: Larger sample sizes produce narrower confidence intervals, as the standard error (SD/√n) decreases with increasing n.