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:

- (i) The level of significance used, and
- (ii) The alternative hypothesis, whether it is two tailed or single tailed.

As has been pointed out earlier, for large samples, the standardized variable corresponding to the statistic t viz. :

------------------------(a)

Asymptotically as n à ∞. The value of Z given by (a) under the null hypothesis is known as test statistic. The critical value of the test statistics at level of significance α for a two- tailed test is given by Zα where Zα is determined by the equation

P(|Z|> Zα) = α ------------------(1)

That is Zα is the value so that the total area of the critical region on both tails is α. Since normal probability curve is a symmetrical curve, from (1), we get

P(Z > Zα) + P(Z < -Zα) = α

- è P (Z > Zα) + P(Z >Zα) = α
- è 2P (Z > Zα) = α
- è P( Z > Zα) = α/2

That is the area of each tail is α/2. Thus Zα is the value such that area to the right of Zα is α/2 and to the left of - Zα is α/2.

In case of single tail alternative, the critical value Zα is determined so that total area to the right of it is α and for left tailed test the total area to the left of - Zα is α.

Thus the significant or critical value of Z for a single tailed test (left or right) at level of significance ‘α’ is same as the critical value of Z for a two tailed test at level of significance ‘2α’.

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- Procedure for testing of hypothesis
- Test Of Significance For Large Samples
- Sampling Of Attributes
- Test of significance for difference of proportions
- Sampling of Variables
- Standard Error Of Sample Mean
- Test Of Significance For Single Mean
- Test Of Significance For Difference Of Means
- Test Of Significance For The Difference Of Standard Deviations

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