Whenever you conduct a hypothesis test, you will get a test statistic as a result. To determine if the results of the hypothesis test are statistically significant, you can compare the test statistic to a** 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, μ, σ)**

where:

**probability:**the significance level**μ:**population mean**σ:**population standard deviation

You can access this function on a TI-84 calculator by pressing 2nd and then pressing vars. This will take you to a **DISTR **screen where you can then use **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: **Find the Z critical value for a left-tailed test with a significance level of 0.05.

**Answer: **invNorm(.05, 0, 1) = **-1.6449**

**Interpretation: **If the test statistic of the test is less than **-1.6449**, then the results of the test are statistically significant at α = 0.05.

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

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

**Answer: **invT(1-.10, 0, 1) = **1.2816**

**Interpretation: **If the test statistic of the test is greater than **1.2816**, then the results of the test are statistically significant at α = 0.10.

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

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

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

**Interpretation: **Since this is a two-tailed test, we actually have two critical values: **-1.96** and **1.96**. If the test statistic of the test is less than **-1.96 **or greater than **1.96**, then the results of the test are statistically significant at α = 0.05.