O: Statistical hypothesis testing flashcards

Topic 16: O: Statistical hypothesis testing

Null and alternative hypotheses

H₀: the starting belief, one value of the parameter (p = 0.3, μ = 50, ρ = 0). H₁: uses <, > or ≠, and is accepted if the evidence is strong enough.

Significance level

The threshold probability for rejecting H₀; it is the probability of incorrectly rejecting H₀.

Critical region, critical value and acceptance region

Critical region: values of the test statistic that lead to rejecting H₀. Critical value: the first value inside it. Acceptance region: everything else.

p-value, and the decision rule

p-value: P(result at least as extreme as observed, assuming H₀ is true). Reject H₀ if the p-value < the significance level, or the test statistic is in the critical region.

1-tail vs 2-tail test

1-tail: H₁ is one-directional (< or >). 2-tail: H₁ uses ≠, and the significance level is split equally between the two tails.

How should the conclusion of a hypothesis test be worded?

In context and without certainty: "there is (or is not) sufficient evidence to suggest…". Never "accept H₁" or "prove H₀".

Distribution of the sample mean of n values from N(μ, σ²)

X̄ ~ N(μ, σ²/n). For σ = 6 and n = 9, the standard deviation of X̄ is 6/3 = 2.

Test statistic for a test of a normal mean

z = (x̄ − μ₀)/(σ/√n), where μ₀ is the value in H₀.

Hypothesis test for correlation

H₀: ρ = 0 (no correlation in the population); H₁: ρ > 0, ρ < 0 or ρ ≠ 0. Compare the sample product moment correlation coefficient r with the critical value (or use the p-value).

Binomial test: which probability do you compare for H₁: p > p₀ and for H₁: p < p₀?

p > p₀: P(X ≥ observed value). p < p₀: P(X ≤ observed value). Both are found under H₀, X ~ B(n, p₀).