P-Value Calculator

The p-value is the probability, assuming the null hypothesis is true, of getting a test statistic at least as extreme as the one you observed. A small p-value means your result would be surprising under H₀.

The usual cutoffs are α = 0.05 and α = 0.01. If p ≤ α, you reject the null hypothesis; if p > α, you fail to reject it. Smaller α means stronger evidence is required.

Two-tailed if your alternative hypothesis only says the parameter differs (either direction); one-tailed if it specifies a direction, like “greater than”. A two-tailed p-value is double the one-tailed one for the same statistic.

Use t when the population standard deviation is estimated from the sample — the usual case in homework. You need the degrees of freedom (at least 1); with large df the t p-value is nearly identical to the z one.

No. Failing to reject H₀ only means the data did not give enough evidence against it — absence of evidence is not evidence of absence. You never “accept” the null hypothesis.