Math

One-sample t-test.

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 · 5 phases

Step by step.

  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

Real-world.

  • 1 Testing whether the average weight of cereal boxes differs from the labeled 16 oz
  • 2 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

Tangled up with.

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

1 unit use this concept.

AP Statistics Inference for Means →