T-Test Calculator

Perform hypothesis testing using the Student's t-distribution.

One-Sample

Two-Sample

Paired

Sample Data (comma-separated):

Hypothesized Mean (μ₀):

Significance Level (α):

Alternative Hypothesis:

Result

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Enter data and calculate

t-Statistic

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Degrees of Freedom

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p-Value

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Critical Value

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Sample Mean

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Sample SD

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95% CI

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Decision

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T-Distribution & T-Test

The t-test determines if there's a significant difference between means. It's used when the population standard deviation is unknown or sample sizes are small.

One-Sample T-Test Formula

t = (x̄ - μ₀) / (s / √n)

Types of T-Tests

Type	Use Case
One-Sample	Compare sample mean to known value
Two-Sample	Compare means of two independent groups
Paired	Compare before/after or matched pairs

Interpreting Results

p < α: Reject null hypothesis (significant difference)
p ≥ α: Fail to reject null (no significant difference)

T-Distribution Properties

Bell-shaped, symmetric around 0
Heavier tails than normal distribution
Approaches normal as df increases

Frequently Asked Questions

When should I use t-test vs z-test?

Use t-test when population standard deviation is unknown or sample size is small (n < 30). Use z-test when population SD is known and sample size is large.

What is the difference between one-tailed and two-tailed tests?

Two-tailed tests check for any difference. One-tailed tests check for difference in a specific direction (greater than or less than).