You can use this student t-test calculator to determine when to reject or fail to reject the null hypothesis given a set of statistics for a sample. Use this student t-test calculator when the population standard deviation is not known. Enter the population mean, sample standard deviation, sample mean, sample size, direction, and level of significance. The calculator will determine the t-score test statistic, the critical t-score(s) based on the level of significance you provide, and the p-value of the test statistic. In addition, this calculator will tell you the conclusion and analyze it, telling you the type of error (type I or type II) and an interpretation of what the error means.

When to Use the T-Test Calculator or the Z-Test Calculator

Case #1 – Use the T-Test calculator under the following conditions:

• You do NOT have the population standard deviation (σ).
• The sample is a simple random sample.

Case #2 – Use the T-Test calculator under the following conditions:

• You have the population standard deviation (σ).
• The sample size, n, is less than or equal to 30.
• The sample is a simple random sample.

Case #3 – Use the z-test calculator under the following conditions:

• You have the population standard deviation (σ).
• The sample size for your data is sufficiently large (n > 30).
• The sample is a simple random sample.

Notice that in all cases, the sample should be a simple, random sample. In summary, use the z-test calculator when you have the population standard deviation (σ) AND n > 30. If either of those conditions are false, use the t-test calculator.

You can also refer to this diagram for help choosing the correct test calculator for the problem you are working on,