T-Test Calculator

This calculator runs a one-sample t-test: T-Statistic is (sampleMean − populationMean) / standardError (line 10), where Standard Error is Sample Standard Deviation divided by the square root of Sample Size (line 9). Sample Mean and Population Mean pull on T-Statistic with the same underlying sensitivity (1/standardError in each direction), but Sample Mean's default of 105 is 5% larger than Population Mean's default of 100, so a proportional nudge to Sample Mean produces a slightly larger absolute swing — not because the formula weighs it more, but because its starting value is bigger. Degrees of Freedom is just Sample Size − 1 (line 11) and, at the default Sample Size of 30, works out to 29 — one short of the engine's own df ≥ 30 threshold for switching to the large-sample normal approximation (line 16).

That means the default calculation actually runs through the small-sample branch (adjustedZ = absT × √(df/(df+1)), line 21), not the "large df" approximation, despite n = 30 being the textbook rule of thumb for when a normal approximation is considered safe. The 95% Margin of Error is always built from a fixed z = 1.96 (line 27) regardless of anything else on the page — this calculator has no confidence-level input to change that.