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     Critical Z-Values for the Normal Distribution

Instructions: Compute critical z-values for the normal distribution probabilities using the form below. Please type significance level \(\alpha\), and indicate the type of tail (left-tailed, right-tailed, or two-tailed)

Significance level (\(\alpha\))
=
Two-Tailed
Left-Tailed
Right-Tailed

Some more information about critical values for the normal distribution probability: Critical values are points at the tail(s) of a certain distribution so that the area under the curve for those points to the tails is equal to the given value of \(\alpha\). For a two-tailed case, the critical values correspond to two points to the left and right of the center of the distribution, with the property that the sum of the area under the curve for the left tail (from the left critical point) and the area under the curve for the right tail is equal to the given significance level \(\alpha\).

For a left-tailed case, the critical value corresponds to the point to the left of the center of the distribution, with the property that the area under the curve for the left tail (from the critical point to the left) is equal to the given significance level \(\alpha\).

For a right-tailed case, the critical value corresponds to the point to the right of the center of the distribution, with the property that the area under the curve for the right tail (from the critical point to the right) is equal to the given significance level \(\alpha\)

The main properties are:

  • If the distribution being analyzed is symmetric, the critical points for the two-tailed case are symmetric with respect to the center of the distribution

  • For a symmetric distribution, finding critical values for a two-tailed test with a signficance of \(\alpha\) is the same as finding one-tailed critical values for a significance of \(\alpha/2\)


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