Calculate confidence intervals for population means (z-test and t-test) and population proportions. Used in surveys, clinical trials, and Australian research.
E.g. survey: 180 of 300 respondents said "Yes"
| Parameter | Value |
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| Level | Lower | Upper | Width |
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A 95% confidence interval means: if we repeated this sampling procedure 100 times, approximately 95 of the resulting intervals would contain the true population parameter. It does NOT mean there's a 95% probability the true value is in this specific interval.
Z-test: Use when population standard deviation (σ) is known, or when n ≥ 30 (Central Limit Theorem). Uses z critical values (e.g. z=1.96 for 95%).
T-test: Use when σ is unknown and estimated by sample SD (s), especially for small samples (n < 30). Uses t critical values with (n−1) degrees of freedom — slightly wider intervals.
The margin of error (E) = critical value × standard error. For a mean: E = z × σ/√n. Increasing sample size by 4× reduces margin of error by half.
The ABS publishes confidence intervals with all survey estimates. For example, the Labour Force Survey reports monthly employment figures with a relative standard error (RSE) and 95% confidence intervals. The NHMRC requires confidence intervals in all clinical research publications.