Confidence Interval Calculator
Calculate confidence intervals for population means or proportions. Enter your data and select the appropriate options to compute the interval.
Understanding Confidence Intervals
A confidence interval gives an estimated range of values which is likely to include an unknown population parameter. The width of the confidence interval gives us some idea about how uncertain we are about the unknown parameter.
Key Concepts:
- Confidence Level: The probability that the confidence interval contains the true population parameter (typically 90%, 95%, or 99%)
- Margin of Error: Half the width of the confidence interval, affected by sample size and variability
- Critical Value: The number of standard errors to go out from the sample statistic (depends on confidence level and distribution)
- Standard Error: The standard deviation of the sampling distribution of a statistic
When to Use Z vs. t Distribution:
- Z-distribution: When population standard deviation is known OR sample size is large (n ≥ 30)
- t-distribution: When population standard deviation is unknown AND sample size is small (n < 30)
Formulas Used:
For Means: CI = x̄ ± (z* or t*) × (σ/√n or s/√n)
For Proportions: CI = p̂ ± z* × √(p̂(1-p̂)/n