Critical Region

The critical region, determined by the significance level

α,

is the set of values that will lead to rejecting the null hypothesis

H_{0} .

In a standard normal distribution, this region is located in the tails of the distribution. The cutoff value of the region is a critical value given by the

z -

value of

α .

The tests of significance — left, right, or two-tail — determine whether there are one or two critical regions.

	Critical Values
Significance Level	Left-Tail Test $H_{a} : μ < k$	Two-Tail Test $H_{a} : μ \neq = k$	Right-Tail Test $H_{a} : μ > k$
$α = 1 %$	$- 2.326$	$\pm 2.576$	$2.326$
$α = 5 %$	$- 1.645$	$\pm 1.960$	$1.645$
$α = 10 %$	$- 1.282$	$\pm 1.645$	$1.282$

This table shows the typical significance levels and their corresponding critical values. It is worth noting that the area of the critical region(s) is equal to the significance level $α .$

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