Critical Value Method

A traditional way of making a hypothesis-testing decision. Computed test statistic is compared with the critical value obtained from a statistical table.

Used when:

• a fixed significance level ($\alpha$) is chosen.
• standard distributions are used.

Appropriate for both one-tailed and two-tailed tests.

For Two-Tailed Tests

Suppose:

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

Reject $H_0$ if $\left\lvert z \right\rvert \gt z_{\alpha/2}$.

For Right-Tailed Tests

Suppose:

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

Reject $H_0$ if $z \gt z_{\alpha}$.

For Left-Tailed Tests

Suppose:

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

Reject $H_0$ if $z \lt -z_{\alpha}$.