Hypothesis testing at A-Level: the wording that gets full marks

Hypothesis testing is the topic where being 90% right earns you 50% of the marks. The maths is often trivial — plug into the calculator, get a p-value. But the *wording* around the maths is where the marks live, and it's remarkably strict.

Here's the phrasing template Edexcel examiners want, sentence by sentence.

The template

Step 1 — State the hypotheses.

• $H_0$: $\mu = 20$ (or whatever the claimed value is)
• $H_1$: $\mu \neq 20$ (two-tailed) or $\mu > 20$ / $\mu < 20$ (one-tailed)

Use $\mu$ for population means, $p$ for proportions. Never use $\bar{x}$ or the sample statistic in the hypotheses — that's the classic half-mark loss.

Step 2 — State the significance level.

"Test at the 5% significance level" or "Using $\alpha = 0.05$".

Step 3 — Calculate the test statistic or p-value.

Show the calculator input. Something like "$Z = \dfrac{22 - 20}{\sigma/\sqrt{n}} = 1.82$".

Step 4 — Compare.

Either "critical value $z_{crit} = 1.96$; since $1.82 < 1.96$..." OR "$p = 0.069 > 0.05$..."

Step 5 — The killer sentence.

This is where the marks live. The examiner wants this EXACT structure:

The half-mark trap

Students routinely write "We accept $H_0$" or "$H_0$ is true". Both lose the interpretation mark.

You can NEVER accept $H_0$. You either reject it or fail to reject it. And you can NEVER call it "true" — statistics is about evidence, not truth.

The other trap: not putting the conclusion in CONTEXT. If the question is about the mean weight of chocolate bars, your conclusion must mention chocolate bars. "We cannot reject $H_0$" alone earns partial marks; "We cannot conclude that the mean chocolate-bar weight differs from 20g" earns full marks.

The one-tailed sign trap

For a one-tailed test, the sign of $H_1$ matches the direction stated in the question. "The claim is that the mean has *increased*" → $H_1: \mu > 20$. Get this backwards and every subsequent mark cascades.

Read the question TWICE. Underline the direction. Write $H_1$ with the sign matching, then check by re-reading the underlined phrase.

A worked example

*A machine is claimed to produce bolts with mean length 5.0 cm. A sample of 25 bolts has mean 5.08 cm with population standard deviation 0.2 cm. Test at the 5% level whether the mean has changed.*

Full-marks answer:

• $H_0: \mu = 5.0$
• $H_1: \mu \neq 5.0$ (two-tailed because "changed" is directionless)
• Significance level $\alpha = 0.05$
• Test statistic: $Z = \dfrac{5.08 - 5.0}{0.2/\sqrt{25}} = 2.0$
• Critical values $\pm 1.96$; since $2.0 > 1.96$, we reject $H_0$.
• Conclusion: There is sufficient evidence, at the 5% level, that the mean bolt length has changed from 5.0 cm.

Notice the conclusion restates the CONTEXT ("mean bolt length") and the DIRECTION of $H_1$ ("has changed"). That's the mark.

Your drill

Take any five hypothesis-testing questions from past papers. Write ONLY the conclusion sentence for each. Mark yourself against the mark scheme with brutal honesty — did you use "reject" / "fail to reject" AND put it in context? If not, rewrite the sentence until you do.

Five sentences a day for a week. Twelve marks recovered on the real paper.