# 8.1.2 Performing a two-tailed one-sample T-test

For a two-tailed one-sample t-test, Excel also provides a specific function: T.INV.2T.

The syntax is: =T.INV.2T(probability, degrees_freedom)

Figure 25 T.INV.2T Function

Where:

- probability: This value represents the cumulative probability for which you want to find the corresponding t-value. It determines the boundary of the t-distribution.
- degrees_freedom: This equals N-1, where N is the sample size. It defines the specific shape of the t-distribution.

Using our previous example of a two-tailed one-sample t-test with α = 5% and 10 degrees of freedom, we would enter: =T.INV.2T(0.05, 10) which returns 2.228

Remember that the T.INV.2T function returns the two-tailed t critical value, which is the absolute value for the positive side of the t-distribution. For a two-tailed test, the t-distribution has both positive and negative critical values. Therefore, when reporting the t critical value, it is necessary to use the ± sign to show both the upper and lower bounds of the critical region.

Thus, the t critical value for two tailed test = ± 2.228

This boundary is crucial because:

- If your calculated t-statistic falls beyond this boundary, you reject the null hypothesis.
- If your t-statistic falls within these boundaries, you fail to reject the null hypothesis.

We can still use T.INV(probability, degrees_freedom) to find t critical value for two-tailed one-sample t-test. You need to modify the probability by dividing the desired significance level by 2 to account for both tails.

For instance, for a two-tailed test with α = 5%:

- =T.INV(0.025, 10) for lower tail
- =T.INV(0.975, 10) for upper tail

OpenLearn - Data analysis: hypothesis testing
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