Hypothesis testing

The topic on one screen

• The null hypothesis $H_0$ contains equality and represents the model being tested. The alternative $H_1$ comes from the claim and decides whether the test is lower-tailed, upper-tailed or two-tailed.
• A significance level is the maximum probability, assuming $H_0$ is true, of rejecting $H_0$ by mistake. For a two-tailed test, share the probability across both tails when constructing a critical region.
• A p-value is the probability, under $H_0$, of a result at least as extreme in the direction of $H_1$. Reject $H_0$ when the p-value is no greater than the significance level.
• For a binomial proportion test, write $X\sim B(n,p_0)$ under $H_0$. For an upper-tail observation $x$, calculate $P(X\geq x)$; for a lower tail, calculate $P(X\leq x)$.
• For a Normal mean test with known, given or assumed variance, $\bar{X}\sim N\left(\mu_0,\dfrac{\sigma^2}{n}\right)$ under $H_0$. Test the sample mean, not a single observation.
• For correlation, use $H_0:\rho=0$ and a contextual alternative. Compare the sample product moment correlation coefficient $r$ with the table value for the stated sample size and tail.
• The final sentence must answer the contextual claim: 'reject $H_0$' alone is not a conclusion, and 'accept $H_0$' overstates what a non-significant result proves.

Where students actually lose marks

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Questions are written in the style of past Edexcel papers (source shown on each) — never copied from them.

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