Confidence Interval Calculator

Calculate confidence intervals for population parameters.

For Mean

For Proportion

Sample Mean (x̄):

Sample Size (n):

Standard Deviation:

SD Type:

Confidence Level:

Confidence Interval

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Enter sample data and confidence level

Lower Bound

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Upper Bound

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Margin of Error

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Critical Value

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Confidence Intervals

A confidence interval provides a range of values that likely contains the true population parameter with a specified level of confidence.

CI = point estimate ± margin of error

For Population Mean

CI = x̄ ± Z*(σ/√n) or x̄ ± t*(s/√n)

Use Z when σ is known and n is large; use t-distribution otherwise.

For Population Proportion

CI = p̂ ± Z*√(p̂(1-p̂)/n)

Critical Values

Confidence Level	Z-Critical Value
90%	1.645
95%	1.96
99%	2.576
99.9%	3.291

Frequently Asked Questions

What does 95% confidence mean?

It means if we repeated the sampling process many times, about 95% of the resulting intervals would contain the true population parameter. It does NOT mean there's a 95% chance the parameter is in this interval.

When should I use t-distribution vs Z?

Use t-distribution when the population standard deviation is unknown (using sample SD) or when the sample size is small (n < 30). Use Z when σ is known and n is large.