*54*

When you conduct a t-test, you will get a test statistic as a result. To determine if the results of the t-test are statistically significant, you can compare the test statistic to a**Â TÂ critical value**. If the absolute value of the test statistic is greater than the T critical value, then the results of the test are statistically significant.

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

**invT(probability, v)**

where:

**probability:**the significance level**v:**the degrees of freedom

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 **invT()**:

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

**Example 1: T Critical Value for a Left-Tailed Test**

**Question:Â **Find the T critical value for a left-tailed test with a significance level of 0.05 and degrees of freedom = 11.

**Answer:Â **invT(.05, 11) = **-1.7959**

**Interpretation:Â **If the test statistic of the t-test is less thanÂ **-1.7959**, then the results of the test are statistically significant atÂ Î± = 0.05.

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

**Question:Â **Find the T critical value for a right-tailed test with a significance level of 0.05 and degrees of freedom = 24.

**Answer:Â **invT(1-.05, 24) = **1.71088**

**Interpretation:Â **If the test statistic of the t-test is greater than **1.71088**, then the results of the test are statistically significant atÂ Î± = 0.05.

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

**Question:Â **Find the T critical value for a two-tailed test with a significance level of 0.05 and degrees of freedom = 13.

**Answer:Â **invT(.05/2, 13) =Â **-2.1604, 2.1604**

**Interpretation: **Since this is a two=tailed test, we actually have two critical values: **-2.1604** andÂ **2.1604**.Â If the test statistic of the t-test is less than **-2.1604Â **or greater thanÂ **2.1604**, then the results of the test are statistically significant atÂ Î± = 0.05.