Track 8 · Hypothesis Testing · Lesson 3 of 14
Test statistics and p-values
Compute a test statistic as a standardised distance from H0, find its p-value for a one- or two-sided alternative, and interpret the p-value correctly.
A courier wants to know whether its new routing system has changed the old 45-minute average delivery time. A sample of 25 deliveries averages 42.6 minutes. Is 2.4 minutes a lot? That depends on how much delivery times vary and how many we measured — the test statistic and p-value put that judgement on a common scale.
A test statistic measures how far the data are from what H0 predicts, in units of standard error. Almost every test in this track has the same shape:
Included with a Formula Quest membership
It has 7 graded exercises with feedback, hints and worked solutions. After it you will be able to:
- Compute a test statistic as (estimate − null value) / standard error
- Find one- and two-sided p-values from the t and normal distributions
- State the meaning of a p-value as a probability about data computed under H0
- Recognise and correct the classic p-value misreadings