Step-by-Step Calculation
Master Formula
CI = x̄ ± Z × (σ / √n)
Step 1: Identify Z-Score
Find the critical value (Z) for the chosen 95% confidence level.
Z = 1.960
Step 2: Standard Error (SE)
Calculate the standard error of the mean: SE = σ / √n
SE = 15 / √30 = 2.739
Step 3: Margin of Error (ME)
Multiply Z-score by Standard Error: ME = Z × SE
ME = 1.960 × 2.739 = 5.368
Step 4: Final Interval
Add and subtract ME from the sample mean: [x̄ - ME, x̄ + ME]
[44.632, 55.368]
Visual Number Line
The axis scale is locked to a fixed window around the mean, allowing you to visually see the interval width expand and contract predictably.