gen-define-a-p-value-and-give-one-short-worked-example-fdba

Define a p-value and give one short worked example.

# P-Value Definition A **p-value** is the probability of obtaining results as extreme as, or more extreme than, the observed results, assuming the null hypothesis is true. In simpler terms: "If there were really no effect, what's the chance we'd see data this extreme just by random chance?" ## Worked Example **Scenario:** A coin is flipped 100 times and lands on heads 60 times. Is this a fair coin? **Setup:** - Null hypothesis (H₀): The coin is fair (p = 0.5) - Observed result: 60 heads out of 100 flips **Calculation:** Under a fair coin, we expect 50 heads. We need the probability of getting ≥60 heads OR ≤40 heads (two-tailed test) purely by chance. Using the binomial distribution: - P(X ≥ 60 or X ≤ 40 | p = 0.5, n = 100) ≈ 0.057 **P-value = 0.057** **Interpretation:** There's a 5.7% chance of seeing results this extreme if the coin were actually fair. At the common α = 0.05 significance level, we would *not* reject the null hypothesis (since 0.057 > 0.05), meaning we don't have strong enough evidence to conclude the coin is unfair.