| Exam Board | OCR |
|---|---|
| Module | AS Pure (AS Pure Mathematics) |
| Year | 2017 |
| Session | Specimen |
| Marks | 8 |
| Topic | Hypothesis test of binomial distributions |
| Type | One-tailed hypothesis test (upper tail, H₁: p > p₀) |
| Difficulty | Standard +0.3 This is a straightforward one-tailed binomial hypothesis test with clear parameters (n=450, p=0.097) and standard procedure. Part (a) requires routine application of the normal approximation or binomial test at 10% level. Part (b) tests understanding of independence assumptions, which is a standard validity check. Slightly above average difficulty due to the two-part structure and need to interpret validity, but still a textbook-style question with no novel problem-solving required. |
| Spec | 2.05b Hypothesis test for binomial proportion2.05c Significance levels: one-tail and two-tail |
12 It is known that under the standard treatment for a certain disease, $9.7 \%$ of patients with the disease experience side effects within one year. In a trial of a new treatment, 450 patients with this disease were selected and the number, $X$, that experienced side effects within one year was noted. It was found that 51 of the 450 patients experienced side effects within one year.
\begin{enumerate}[label=(\alph*)]
\item Test, at the $10 \%$ significance level, whether the proportion of patients experiencing side effects within one year is greater under the new treatment than under the standard treatment.
\item It was later discovered that all 450 patients selected for the trial were treated in the same hospital.
Comment on the validity of the model used in part (a).
\end{enumerate}
\hfill \mbox{\textit{OCR AS Pure 2017 Q12 [8]}}