Confidence intervals

Learning objectives

• Build a t confidence interval for a mean using free-spreadsheet functions.
• Build a robust interval for a proportion.
• Interpret the confidence level correctly.

Core idea

An interval estimate = point estimate ± critical value × standard error. In the long run, 95% of such intervals contain the true parameter; a single interval either does or does not.

Spreadsheet lab

• Mean CI: =AVERAGE(A2:A31) ± =T.INV.2T(0.05, n-1) * =STDEV.S(A2:A31)/SQRT(n).
• Proportion (Wilson): centre = (x + z²/2)/(n + z²); half-width uses SQRT(p̂(1−p̂)/n + z²/(4n²)).
• z at 95% = =NORM.S.INV(0.975) ≈ 1.96.

Garment-factory example

Twenty seam-strength readings give mean 172 N, SD 14 N, n = 20. 95% CI = 172 ± T.INV.2T(0.05,19) × 14/√20 = 172 ± 6.55 N → (165.5, 178.5) N.

Method

1. State parameter, n, method and confidence level.
2. Compute point estimate and standard error.
3. Report interval with units and sample size.

Common mistakes

• Saying 'the true mean has a 95% probability of being inside'.
• Using normal approximation for proportions near 0 or 1.