Finding the Critical Values for specific α Values, Using Table E

Step 1  Draw the figure and indicate the appropriate area.

a. If the test is left-tailed , the critical region, with an area equal to α, will be on the left side of the mean.

b. If the test is right-tailed, the critical region, with an area equal to α, will be on the  right side of the mean.

c. If the test is two-tailed, α must be divided by 2, one-half of the area will be to the right of the mean, and one-half  will be to the left of the mean.

Step 2  For one-tailed test, subtract the area (equivalent to  α ) in the critical region from 0.5000, since Table E gives the area under the normal distribution curve between 0 and any z to the right of 0.  For a two-tailed test, subtract the area (equivalent to   α over 2) from 0.5000.

Step 3  Find the area in Table E corresponding to the value obtained in Step2.  If the exact value cannot be found in the table, use the closest value.

Step4  Find the z value that corresponds to the area.  This will be the critical value.

Step 5  Determine the sign of the critical value for a one-tailed test

a.  If the test is left-tailed, the critical value will be negative.

b.  If the test is right-tailed, the critical value will be positive.

 For a two-tailed test, one value will be positive and the other negative.

by: Marie Louissie Ynez U. Lavega