The value of test statistic which separates the critical region and the acceptance region is called the critical value or significant value.

It depends upon :

**1)** The level of significance used and

**2)** The alternative hypothesis, whether it is two-tailed or single-tailed.For large samples ($n$ > 30), the standardised variable corresponding to the statistic $t$,

$Z$ =

$\frac{t - E(t)}{S.E.(t)}$ $\sim$ $N$(0,1) asympotically as n tends to infinity.

Value of $Z$ under the null hypothesis is known as test statistic. The critical value of the test statistic at level of significance $\alpha$ for a two tailed test is given by $Z_{\alpha}$, where $Z_{\alpha}$ is determined by the equation:

$P$(|$Z$| > $Z_{\alpha}$) = $\alpha$

$Z_{\alpha}$ is the value so that the total area of the critical region on both tails is $\alpha$. Since normal probability curve is a symmetrical curve.

$P$($Z$ > $Z_{\alpha}$) + $P$($Z$ < - $Z_{\alpha}$) = $\alpha$

= $P$($Z$ > $Z_{\alpha}$) + $P$($Z$ > $Z_{\alpha}$) = $\alpha$

**(By symmetry)**

2$P$ ($Z$ > $Z_{\alpha}$) = $\alpha$

$P$ ($Z$ > $Z_{\alpha}$) =

$\frac{\alpha}{2}$In case of single tail alternative we have,

Right tailed test : $P$($Z$ > $Z_{\alpha}$) = $\alpha$

Left tailed test : $P$($Z$ < - $Z_{\alpha}$) = $\alpha$

**Critical values of $Z$ at commonly used levels of significance for both two tailed and single tailed tests using normal probability tables are listed below:**