Confidence Interval Calculator
Calculator to compute the confidence interval or margin of error of a sample based on the desired confidence level.
How to Use the Confidence Interval Calculator
Enter sample estimate, variability measure, confidence level, and sample size to compute confidence interval bounds.
Uncertainty Quantification
Confidence intervals express estimate precision as a range.
Width Drivers
Sample size, variability, and confidence level jointly set interval width.
Interpretation Precision
Frequentist CI interpretation is method-based, not single-interval probability.
Method Selection
Correct critical-value choice depends on variance knowledge and sample size.
Design Integrity
Sampling quality is as important as formula correctness.
Frequently Asked Questions
What is confidence interval?+
A range that likely contains the true population parameter under repeated sampling.
Does 95% CI mean 95% chance parameter is in this interval?+
Strictly, it means the method captures true value in 95% of repeated samples.
How does sample size affect CI?+
Larger sample size usually narrows interval width.
How does variability affect CI?+
Higher variability widens confidence intervals.
What is standard error?+
Standard error quantifies sampling uncertainty of an estimate.
When use z vs t critical values?+
Use t when population variance is unknown and sample is limited.
Can CI prove practical significance?+
CI indicates estimation uncertainty, not necessarily practical importance.
Does overlapping CI imply no difference?+
Not always; formal comparison tests may still detect differences.
Can non-random samples invalidate CI?+
Yes, sampling bias can make intervals misleading.
Is CI same as prediction interval?+
No, prediction intervals target future observations and are typically wider.
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