Lesson 30 of 1524
Hypothesis testing with one sample
Reject the null when the p-value is at most α. A large p-value is not proof that the null is true.
Practice this chapterThe null hypothesis is the claim you test, often a statement of no effect or of a specific parameter value. The alternative is what you are looking for: less than, greater than, or different from.
The p-value is the chance of a result at least this extreme if the null is true. You reject the null when p ≤ α. Failing to reject is not the same as accepting the null. Rejecting a true null is a Type I error, and its rate is α. Failing to reject a false null is a Type II error.
The decision
Reject H₀ when p ≤ α
Otherwise, fail to reject H₀.
Worked example
The p-value is 0.03 and α is 0.05. What is the decision?
- 1The decision rule is: reject H₀ when the p-value is less than or equal to α. Otherwise, fail to reject H₀.
- 2Compare the two numbers you were given: p = 0.03 and α = 0.05.
- 30.03 is smaller than 0.05, so p ≤ α.
- 4The decision is to reject H₀. The p-value is the chance of a result at least this extreme if H₀ were true. It is not the probability that H₀ itself is true.
Result: Reject H₀
Why. 0.03 is at or below the cutoff 0.05, and that is exactly the condition for rejecting the null. A p-value of 0.12 with the same α would fail to reject, because 0.12 is larger than 0.05.
“Accept the null” is the sentence this course avoids. The data may simply be too weak to reject it.
Practice margin
This chapter
A fresh set from this chapter only. Choose 10 or 20. Multiple choice and fill-in, with no repeat inside the set.