Statistics · Hypothesis testing
Chapter 1 · 3
The idea
One-tailed tests (the probability method)
Carrying out a one-tailed binomial hypothesis test by the probability (p-value) method: assume H0, model X ~ B(n, p0), find the probability of a result at least as extreme as the one observed in the direction of H1 — P(X ≥ x) for an upper test or P(X ≤ x) for a lower test — compare it with the significance level, and write a full conclusion in context.
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Statistics · Hypothesis testing
One-tailed tests (the probability method)
Carrying out a one-tailed binomial hypothesis test by the probability (p-value) method: assume H0, model X ~ B(n, p0), find the probability of a result at least as extreme as the one observed in the direction of H1 — P(X ≥ x) for an upper test or P(X ≤ x) for a lower test — compare it with the significance level, and write a full conclusion in context.
Why it works
The logic of the tail
A coin lands heads 15 times out of 20. Biased, or just lucky? To test a directional claim, we assume the null hypothesis is true — the coin is fair — and ask how likely a result as extreme as the observed one would be. If that is below the significance level, the data are too surprising for to stand.Why "or more extreme"? A test asks whether the result is unusually high (or low), so we measure the whole tail from the observed value outward, not just the single value . That tail probability is the p-value.
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