*35*

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 a**Â 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.