Key Idea: A confidence interval is a believable range for the true population mean. It is the sample mean plus or minus a margin of error, and you build it on the GDC.
| Item | Detail |
|---|---|
| Formula | CI = x̄ ± t*·sₙ-₁/√n |
| Degrees of freedom | df = n − 1 |
| GDC t-interval | Enter x̄, sₙ-₁, n and the C-Level; read (a, b) |
Reading the interval
- Bigger n → narrower (more precise).
- Higher confidence → wider (safer but vaguer).
- Inside the interval = plausible. Outside = evidence against the claim.
- Always use the unbiased standard deviation.
Check where the claimed value sits: inside the interval or outside it.
20 bags give x̄ = 1.502 kg and a 95% interval of (1.496, 1.508). Is 1.500 kg plausible? Yes, it lies inside.
A sample has n = 20. What is df? 19.
You change from 95% to 99% confidence. What happens to the width? It gets wider.
A label claims 1.510 kg. What do these data suggest? 1.510 is outside, so the data are evidence against the label.