Type I and Type II errors
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All 8 Flashcards — Type I and Type II errors
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Question
What is a Type I error?
Answer
Rejecting H₀ when H₀ is actually true (a false alarm — concluding there's an effect when there isn't).
Question
What is a Type II error?
Answer
Failing to reject H₀ when H₀ is actually false (a miss — concluding there's no effect when there is one).
Question
What is P(Type I error)?
Answer
It equals the significance level α (e.g. 0.05). Computed from the H₀ distribution / critical region.
Question
What is P(Type II error), and what do you need to compute it?
Answer
β = P(not rejecting H₀ | the alternative is true). You need a SPECIFIC alternative value, and you use that distribution.
Question
What is a critical (rejection) region?
Answer
The set of extreme outcomes for which you reject H₀. α = P(landing in it when H₀ is true).
Question
Which distribution gives α, and which gives β?
Answer
α comes from the H₀ distribution; β comes from the alternative (H₁) distribution.
Question
How do Type I and Type II errors trade off?
Answer
Lowering α shrinks the critical region, which makes a Type II error more likely (β rises), and vice versa.
Question
For X ~ B(20, 0.5), test H₁: p > 0.5, reject if X ≥ 15. What is P(Type I error)?
Answer
P(X ≥ 15 | p = 0.5) = 1 − P(X ≤ 14) ≈ 0.0207.
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Topic 4.18 hub
t & z tests, errors (HL only)
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