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# How to Find the Z Critical Value on a TI-84 Calculator

Whenever you conduct a hypothesis test, you will get a test statistic as a result.Â To determine if the results of the hypothesis test are statistically significant, you can compare the test statistic to aÂ Z critical value. If the absolute value of the test statistic is greater than the Z critical value, then the results of the test are statistically significant.

To find the Z critical value on a TI-84 calculator, we can use the following function:

invNorm(probability, Î¼, Ïƒ)

where:

• probability: the significance level
• Î¼:Â population mean
• Ïƒ: population standard deviation

You can access this function onÂ a TI-84 calculator by pressingÂ 2ndÂ and then pressingÂ vars. This will take you to aÂ DISTRÂ screen where you can then useÂ invNorm():

This tutorial shares several examples of how to use the invNorm() function to find Z critical values on a TI-84 calculator.

### Example 1: Z Critical Value for a Left-Tailed Test

Question:Â Find the Z critical value for a left-tailed test with a significance level of 0.05.

Answer:Â invNorm(.05, 0, 1) = -1.6449

Interpretation:Â If the test statistic of the test is less thanÂ -1.6449, then the results of the test are statistically significant atÂ Î± = 0.05.

### Example 2: Z Critical Value for a Right-Tailed Test

Question:Â Find the Z critical value for a right-tailed test with a significance level of 0.10.

Answer:Â invT(1-.10, 0, 1) = 1.2816

Interpretation:Â If the test statistic of the test is greater than 1.2816, then the results of the test are statistically significant atÂ Î± = 0.10.

### Example 3: Z Critical Value for a Two-Tailed Test

Question:Â Find the Z critical value for a two-tailed test with a significance level of 0.05.

Answer:Â invNorm(.05/2, 0, 1) =Â -1.96, 1.96

Interpretation: Since this is a two-tailed test, we actually have two critical values: -1.96 andÂ 1.96.Â If the test statistic of the test is less than -1.96Â or greater thanÂ 1.96, then the results of the test are statistically significant atÂ Î± = 0.05.