Null and alternative hypotheses, one- and two-tailed tests, significance levels and critical regions, hypothesis tests for a binomial proportion, and for a correlation coefficient and a normal mean.

What this dot point is asking

Edexcel wants you to set up null and alternative hypotheses, carry out one- and two-tailed tests at a stated significance level, find and use critical regions, test a hypothesis about a binomial proportion $p$, test a sample correlation coefficient against zero, and test the mean of a normally distributed variable.

The answer

Hypotheses and significance

A strategy for any hypothesis test

Every test on the paper follows the same five steps. First, define the parameter and state $H_0$ and $H_1$, deciding whether the alternative is one-tailed or two-tailed from the wording. Second, state the distribution of the test statistic assuming $H_0$ is true, such as $X \sim B(n, p_0)$. Third, calculate the probability of a result as extreme as, or more extreme than, the one observed (or find the critical region). Fourth, compare with the significance level. Fifth, state the conclusion in the context of the question, not just "reject $H_0$". The wording "greater than" or "less than" signals a one-tailed test, while "changed" or "different from" signals a two-tailed test.

Critical regions

A binomial test

Examples in context

Try this

Q1. State suitable hypotheses for a two-tailed test that a proportion has changed from $0.3$. [2 marks]

• Cue. $H_0: p = 0.3$ and $H_1: p \ne 0.3$.

Q2. For $X \sim B(10, 0.2)$, $H_0: p = 0.2$, $H_1: p > 0.2$ at $5\%$, you observe $X = 5$. Given $P(X \ge 5) \approx 0.0328$, state the conclusion. [3 marks]

• Cue. $0.0328 < 0.05$, so reject $H_0$: evidence that $p$ has increased.