Hypothesis testing helps decide whether an observed difference is probably real or whether it could easily be explained by randomness. This matters in product experiments, business reporting, and model comparison.## Core Terms- Null hypothesis ($H_0$): no effect or no difference- Alternative hypothesis ($H_1$): the competing claim- p-value: how surprising the data would be if $H_0$ were true- $\alpha$: the cutoff used to judge significancemermaidflowchart LR A[Define H0 and H1] --> B[Collect data] --> C[Compute statistic] --> D[Compute p-value] --> E[Decision]Alt text: Hypothesis testing moves from a claim to data, then to a statistic, a p-value, and a decision.## Worked Example 1: Coin FlipIf a coin shows 8 heads in 10 flips, we can test whether that is surprisingly far from a fair coin.## Worked Example 2: A/B TestIf page A converts 50 of 1000 visitors and page B converts 62 of 1000, we can estimate whether page B is meaningfully better or whether the difference could be sampling noise.:::{admonition} Important caution:class: tipA significant result is not automatically a large or valuable result. Practical importance still matters.:::## Guided Practice1. What does the p-value tell you?2. Why is rejecting $H_0$ not the same as proving $H_1$?3. Why should a business team still care about effect size?