Practice Flashcards
What does the p-value of a hypothesis test measure?
Track your progress — Sign up free to save your progress and get smart review reminders based on spaced repetition.
All Flashcards in Topic 4.18
Below are all 16 flashcards for this topic. Sign up free to track your progress and get personalized review schedules.
4.18.18 cards
What does the p-value of a hypothesis test measure?
The probability of getting data at least this extreme if H₀ were true. Small p = the data are surprising under H₀.
State the decision rule for a hypothesis test.
p < α → reject H₀; p ≥ α → fail to reject H₀ (α = significance level).
When do you use a z-test vs a t-test?
z-test when the population σ is known; t-test when σ is unknown (you only have the sample sd) — the usual case.
One-sample vs two-sample test?
One-sample: compare one group's mean to a fixed claimed value. Two-sample: compare two independent groups' means.
When is a test one-tailed vs two-tailed?
One-tailed for a directional H₁ (μ < or μ >); two-tailed for H₁: μ ≠ (a difference either way).
What is a paired (matched) t-test for?
When the same subjects are measured twice (before/after). Test the mean of the differences d: H₀: μ_d = 0.
Why must you never say you 'accept H₀'?
A test can only fail to find evidence against H₀ — absence of evidence isn't proof. Say 'do not reject H₀'.
Where do the final marks in an AI hypothesis-test question usually sit?
In the in-context conclusion — naming the real quantities (bottles, runners…), not just 'reject H₀'.
4.18.28 cards
What is a Type I error?
Rejecting H₀ when H₀ is actually true (a false alarm — concluding there's an effect when there isn't).
What is a Type II error?
Failing to reject H₀ when H₀ is actually false (a miss — concluding there's no effect when there is one).
What is P(Type I error)?
It equals the significance level α (e.g. 0.05). Computed from the H₀ distribution / critical region.
What is P(Type II error), and what do you need to compute it?
β = P(not rejecting H₀ | the alternative is true). You need a SPECIFIC alternative value, and you use that distribution.
What is a critical (rejection) region?
The set of extreme outcomes for which you reject H₀. α = P(landing in it when H₀ is true).
Which distribution gives α, and which gives β?
α comes from the H₀ distribution; β comes from the alternative (H₁) distribution.
How do Type I and Type II errors trade off?
Lowering α shrinks the critical region, which makes a Type II error more likely (β rises), and vice versa.
For X ~ B(20, 0.5), test H₁: p > 0.5, reject if X ≥ 15. What is P(Type I error)?
P(X ≥ 15 | p = 0.5) = 1 − P(X ≤ 14) ≈ 0.0207.
Topic 4.18 study notes
Full notes & explanations for t & z tests, errors (HL only)
Math AI exam skills
Paper structures, command terms & tips
Want smart review reminders?
Sign up free to track your progress. Our spaced repetition algorithm will tell you exactly which cards to review and when.
Start Free