One-sided t test: worked example
In a one-sided test only one direction counts, so compare t, not |t|, with the critical value.
Worked example
Test whether mean study time exceeds 20 minutes (H₀: μ ≤ 20, H₁: μ > 20). Sample: n = 25, x̄ = 19.70, s = 5. α = 5%, critical value t = 1.711.
Worked solution
- 1.t = (x̄ − μ₀) / (s / √n) = (19.70 − 20) / (5 / 5) = -0.30
- 2.t = -0.30 ≤ 1.711 → do not reject H₀
Typical mistake: Comparing |t| in a one-sided test; for H₁: μ > μ₀ only large positive values count.
Your turn
Three problems of exactly this type, each time with new numbers. Comma or point; fractions like 1/6 work too.
Task
Test whether mean study time exceeds 20 minutes (H₀: μ ≤ 20, H₁: μ > 20). Sample: n = 25, x̄ = 23.44, s = 8. α = 5%, critical value t = 1.711.
Test statistic t (2 decimal places)
Decision
Comma or point; fractions like 1/6 work too.
Formulas for this topic
- 1. State H₀ and H₁, choose α
- 2. Test statistic: z = (x̄ − μ₀) / (σ / √n) or t = (x̄ − μ₀) / (s / √n)
- 3. Compare with the critical value (two-sided |z|, one-sided only in the direction of H₁)
- 4. Decide: reject or do not reject H₀
Typical mistake: Comparing |t| in a one-sided test; for H₁: μ > μ₀ only large positive values count.
Frequently asked questions
What is the typical mistake in "One-sided t test: worked example"?
Comparing |t| in a one-sided test; for H₁: μ > μ₀ only large positive values count.
What is a type I error?
Rejecting H₀ although it is true; its probability is at most α.