| Exam Board | Edexcel |
|---|---|
| Module | S2 (Statistics 2) |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Hypothesis test of binomial distributions |
| Type | One-tailed hypothesis test (upper tail, H₁: p > p₀) |
| Difficulty | Standard +0.3 This is a straightforward binomial hypothesis test with clearly defined parameters (n=25, p=0.8 under H₀). Part (a) requires standard one-tailed test mechanics that S2 students practice extensively. Part (b) asks for basic interpretation about sample size and significance levels—conceptually simple. The question is slightly easier than average because it's a textbook application with no tricky setup or unusual complications. |
| Spec | 5.05b Unbiased estimates: of population mean and variance |
| Answer | Marks | Guidance |
|---|---|---|
| (a) \(X \sim B(25, p)\) | B1 B1 | |
| \(H_0: p = 0.8\) \(H_1: p > 0.8\) | B1 B1 | |
| Assuming \(H_0\), \(P(24 \text{ or more people recovering within 6 hours}) = P(X \leq 1) \text{ in } B(25, 0.2) = 0.0274 < 5\%\) so reject \(H_0\) at 5% level | M1 M1 A1 A1 | |
| (b) Yes: at 1% level, do not reject \(H_0\), i.e. new drug is no better | M1 A1 | |
| Do more tests, to get more conclusive answer | B1 | Total: 9 |
(a) $X \sim B(25, p)$ | B1 B1 |
$H_0: p = 0.8$ $H_1: p > 0.8$ | B1 B1 |
Assuming $H_0$, $P(24 \text{ or more people recovering within 6 hours}) = P(X \leq 1) \text{ in } B(25, 0.2) = 0.0274 < 5\%$ so reject $H_0$ at 5% level | M1 M1 A1 A1 |
(b) Yes: at 1% level, do not reject $H_0$, i.e. new drug is no better | M1 A1 |
Do more tests, to get more conclusive answer | B1 | **Total: 9**
---A pharmaceutical company produces an ointment for earache that, in 80\% of cases, relieves pain within 6 hours. A new drug is tried out on a sample of 25 people with earache, and 24 of them get better within 6 hours.
\begin{enumerate}[label=(\alph*)]
\item Test, at the 5\% significance level, the claim that the new treatment is better than the old one. State your hypotheses carefully. [6 marks]
A rival company suggests that the sample does not give a conclusive result;
\item Might they be right, and how could a more conclusive statement be achieved? [3 marks]
\end{enumerate}
\hfill \mbox{\textit{Edexcel S2 Q3 [9]}}