P-Value Calculator

1. Choose Z-score or T-score.Use Z when you know the population standard deviation or have a large sample (n > 30). Use T for small samples when population std dev is unknown.
2. Enter your test statistic. This is the value you calculated from your hypothesis test.
3. For T-score, enter degrees of freedom (usually sample size minus 1).
4. Select the test type: two-tailed for testing if a parameter differs from a value in either direction, left-tailed if testing for less than, right-tailed for greater than.
5. Read the p-value and whether the result is statistically significant at the 0.05 and 0.01 levels.

P-value is the probability of observing a result at least as extreme
as your test statistic, assuming the null hypothesis is true.

Two-tailed:   p = 2 × min(CDF(z), 1 - CDF(z))
Right-tailed: p = 1 - CDF(z)
Left-tailed:  p = CDF(z)

Where CDF(z) = area to the left of z under the normal curve.

Common Z critical values:
  α = 0.10 → |z| > 1.645
  α = 0.05 → |z| > 1.960
  α = 0.01 → |z| > 2.576

Example: z = 1.96, two-tailed test
  CDF(1.96) ≈ 0.9750
  p = 2 × min(0.9750, 1 - 0.9750)
    = 2 × min(0.9750, 0.0250)
    = 2 × 0.0250 = 0.05
  Exactly at the boundary of significance at α = 0.05.