gen-define-hypothesis-testing-and-give-one-short-worked-example-72a5

Define hypothesis testing and give one short worked example.

# Hypothesis Testing **Hypothesis testing** is a statistical method used to make decisions about a population parameter based on sample data. It involves: 1. Setting up two competing hypotheses (null and alternative) 2. Collecting sample data 3. Calculating a test statistic 4. Determining whether to reject the null hypothesis based on the evidence --- ## Worked Example **Claim:** A coffee shop claims their average cup contains 300ml. You suspect it's less. **Step 1: Set up hypotheses** - H₀ (null): μ = 300ml - H₁ (alternative): μ < 300ml **Step 2: Collect data** - Sample: 25 cups, mean = 295ml, standard deviation = 10ml - Significance level: α = 0.05 **Step 3: Calculate test statistic** - Use t-test: t = (x̄ - μ)/(s/√n) - t = (295 - 300)/(10/√25) = -5/2 = **-2.5** **Step 4: Make decision** - Critical value for t₂₄ at α = 0.05 (one-tailed): -1.711 - Since -2.5 < -1.711, we **reject H₀** **Conclusion:** There is significant evidence that the average cup contains less than 300ml.