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