P-Value Method

An alternative to the critical value method.

Suitable test statistic is calculated. The probability of observing a test statistic as extreme as or more extreme than the one calculated from the sample data, assuming $H_0$ is true. If the probability is less than $\alpha$ , reject $H_0$ .

Reject $H_0$ if the p-value is less than $\alpha$ .

For Two-Tailed Tests

When:

2 \times P(Z \gt \left\lvert z \right\rvert)

Here:

$H_0$: $\mu = \mu_0$
$H_1$: $\mu \neq \mu_0$

P-value is equal to $2 \times P(Z \gt \left\lvert z \right\rvert)$ .

For Right-Tailed Tests

When:

P(Z \gt z)

Here:

$H_0$: $\mu \leq \mu_0$
$H_1$: $\mu \gt \mu_0$

P-value is equal to $P(Z \gt z)$ .

For Left-Tailed Tests

When:

P(Z \lt -z)

Here:

$H_0$: $\mu \geq \mu_0$
$H_1$: $\mu \lt \mu_0$

P-value is equal to $P(Z \lt -z)$ .

Written by

Sahithyan K.

November 3, 2026 1 min read

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