t-Table (Student's t Distribution)

Interactive t-Table Calculator

Student’s t-Distribution Table

The t-table provides critical values for the t-distribution, used when the population standard deviation is unknown and the sample size is small.

How to Use This Table

1. Calculate degrees of freedom: df = n - 1 (for one-sample) or df = n₁ + n₂ - 2 (for two-sample)
2. Choose your significance level (α) and whether the test is one-tailed or two-tailed
3. Find the intersection of df row and α column

Critical Values (Upper Tail)

This table gives t-values where P(T > t) = α (area in the upper tail).

Common Confidence Interval Values

For two-tailed tests (most common for confidence intervals):

Two-Tailed Critical Values

For two-tailed tests, use these columns:

When to Use t vs z

Degrees of Freedom

Example: Using the t-Table

Problem: A sample of 16 students has a mean test score of 75. Test if this differs from the population mean of 70 at α = 0.05 (two-tailed).

Solution:

1. df = n - 1 = 16 - 1 = 15
2. Two-tailed test at α = 0.05, use column α = 0.025
3. Critical value: t = ±2.131
4. If |calculated t| > 2.131, reject H₀

Related Resources

• T-Test Calculator - Perform t-tests automatically
• t-Distribution Lesson - Understand when and why to use t
• Z-Table - For large samples or known σ
• Confidence Intervals - Building intervals with t