One-sample t-test

Math

Definition

A hypothesis test used to determine whether a population mean differs from a claimed value when the population standard deviation is unknown and the sample size is small. It uses the t-distribution instead of the normal distribution.

How It Works

  1. State the null hypothesis H₀: μ = μ₀ and alternative hypothesis
  2. Check conditions: random sample, approximately normal distribution
  3. Calculate the test statistic: t = (x̄ - μ₀) / (s/√n)
  4. Find the p-value using the t-distribution with n-1 degrees of freedom
  5. Compare p-value to significance level α and make a conclusion

Examples

  • Testing whether the average weight of cereal boxes differs from the labeled 16 oz
  • Determining if a class's mean test score is significantly different from the national average
Key Fact

t = (x̄ - μ₀) / (s/√n), df = n - 1

Related Terms

Hypothesis tests for proportions T-intervals Two-sample t-test Confidence intervals for proportions

Study This Concept

Practice one-sample t-test with free review games in these units:

AP Statistics Unit 7: Inference for Means