Critical value is a term used in statistics that represents the number that must be achieved in order to demonstrate statistical significance. If the critical value is achieved, then the null hypothesis is rejected. A two-tailed test means that the answer should be applicable to both halves of the bell curve, and in a two tailed test the answer must be expressed with both a "+" and "-" sign. For a given alpha value "a," the critical value in a two-tailed test is determined by running the formula (1-a)/2 and then looking up the result on a Z-table
Subtract the alpha value from 1. The alpha value is expressed as decimal less than one. As an example, say the alpha value is .03:
1 - 0.03 =0.97
Divide the result from above by 2. All two-tailed tests must have this step. The result is 0.97/2 or 0.485
Look up the result on a Z-table. If the number itself is not present, then choose the closest match. In the case of the example, 0.485 happens to be displayed on a Z-table.
Find the corresponding number of the row in the far left column, which in this case is 2.1.
Find the corresponding number of the column at the top row, which in this case is 0.07
The critical value is the sum of 2.1 + .07 or 2.17.
Remember to express your answer using a "+" and "-" symbol. The proper answer from above is +/- 2.17.
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