Track 8 · Hypothesis Testing · Lesson 5 of 14
One-sample t-test
Carry out a one-sample t-test from start to finish — hypotheses, assumptions, t, df, p-value, confidence interval and effect size — and state the conclusion in context.
After a routing change, a courier company promised its biggest client that the mean delivery time per parcel would be below 42 minutes. The analyst has four weeks of data from 60 routes. Has the promise demonstrably been kept? The one-sample t-test is the standard tool for comparing a mean with a target.
The one-sample t-test compares the mean of one population, , with a fixed value (a target, a specification, a historical benchmark). Because the population standard deviation is almost never known, we estimate it by the sample standard deviation — and pay for that extra uncertainty by using the t distribution instead of the normal.
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It has 7 graded exercises with feedback, hints and worked solutions. After it you will be able to:
- Run a one-sample t-test: t = (x̄ − μ0)/(s/√n) with n − 1 degrees of freedom
- Match the p-value and the confidence bound to the pre-specified alternative
- Judge the normality condition in light of the sample size
- Report the estimate, interval and effect size, and word a non-significant result without accepting H0