Critical value: Steps to calculate z score for a given significance level
The Critical value is one of the components of hypothesis testing. Here is the complete guide to calculating the Critical value. Let us compute the Critical value for different cases of hypothesis testing.
1. One tail test
1.a Right tailed test:
Assume the Significance level is 5% and the confidence level is 95%.
Step 1: Since it is a right-tailed test consider 95% to calculate the area under the curve.
Refer https://www.ztable.net/ for the z table.
Step 2: Search for .95 in the Z positive table. If you don’t find the exact value 0.95 then consider two values close to 0.95
From the table consider 0.9495 and 0.9505, and then take the average of column values i.e. (.04 +.05)/2 = .045. Now add the column and the row value to find the z-score value. 1.6 + .045 = 1.645.
For right-tailed hypothesis testing, the Critical value of a 5% Significance level is 1.645.
1.b Left tailed test:
Step 1: Since it is a left-tailed test consider 5% to calculate the area under the curve.
Step 2: Search for .05 in the Z negative table. If you don’t find the exact value 0.05 then consider two values close to it
From the table consider 0.0505 and 0.04947, and then take the average of column values i.e. (.04 +.05)/2 = .045. Now add the column and the row value to find the z-score value. -1.6 + -.045 = -1.645.
For right-tailed hypothesis testing, the Critical value of a 5% Significance level is -1.645.
1. Two-tailed test
Method 1: Consider the Significance level (alpha) divided by two.
Continue using the steps mentioned in right-tailed test and left-tailed test for the alpha value 0.025. i.e .025 for left tailed test and 0.975 for right tailed test and find the critical value.
Method 2: Calculate the area under the curve.
Step 1: Consider 95% confidence level to find the critical value using the area under the curve formula.
Step 2: The formula for calculating the area under the curve
where CL is confidence level.
A = (1 + 0.95)/2 = 0.975
Step 3: Search for 0.975 in the Z-positive table.
Consider the z score value present in the corresponding row and column and add them.
z score = 1.9 + .06 = 1.96.
Consider both the sign of z score +1.96 and -1.96.
Hence critical value for 95% confidence interval is +1.96 and -1.96.
EndNote:
I hope this article gives you insight into calculating critical value for different types of hypothesis testing. Please drop your suggestions or queries in the comment section.
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