S7.1StatisticsStretch

Hypothesis Testing

A hypothesis test uses sample evidence to judge a claim about a population. You set up two hypotheses, assume the null is true, then decide whether the data is surprising enough to reject it.

30 min Video by Zeeshan Zamurred Hypothesis Testing

Edexcel AS Level Maths: 7.1 Hypothesis TestingWatch the full walkthrough before the notes below.

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What you'll be able to do

State null and alternative hypotheses
Understand the significance level
Define the test statistic
Outline the logic of a hypothesis test

Null and alternative hypotheses

The $null hypothesis$ $H_{0}$ states the assumed value (e.g. $p = 0.5$ ); the $alternative hypothesis$ $H_{1}$ states what you suspect instead (e.g. $p > 0.5$ ). You test against $H_{0}$ .

H_{0} : p = p_{0} H_{1} : p \neq = p_{0} (or >, <)

Always state both hypotheses in terms of the parameter.

Significance level

The $significance level$ (e.g. 5%) is how strong the evidence must be before you reject $H_{0}$ . It is the probability of wrongly rejecting a true $H_{0}$ , so a smaller level demands stronger evidence.

Tip — The significance level is chosen before seeing the data — typically 5% or 1%.

The logic

Assume $H_{0}$ is true, then find how likely the observed (or more extreme) result would be. If that probability is below the significance level, the result is “surprising”, so you $reject$ $H_{0}$ in favour of $H_{1}$ ; otherwise you do not reject $H_{0}$ . Conclusions are stated in context, never as absolute proof.

Formula recap

H_{0} : p = p_{0}

Null hypothesis (assumed value).

H_{1} : p > p_{0}, <, or \neq =

Alternative hypothesis.

reject H_{0} if P < sig. level

Decision rule.

Common mistakes to avoid

Writing hypotheses about the sample instead of the population parameter.

H₀ and H₁ are statements about the population parameter p.

Saying a test “proves” H₁.

A test gives evidence to reject (or not) H₀ — never absolute proof.

Key takeaways

H₀ states the assumed parameter value; H₁ states the suspected change.
The significance level sets how strong the evidence must be.
Assume H₀, judge how surprising the data is, then reject or not — in context.

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