| Exam Board | OCR |
|---|---|
| Module | H240/02 (Pure Mathematics and Statistics) |
| Year | 2017 |
| Session | Specimen |
| Marks | 5 |
| Topic | Z-tests (known variance) |
| Type | Test using proportion |
| Difficulty | Challenging +1.2 This is a hypothesis testing question requiring students to work backwards from a significance level to find a critical value. It involves calculating a population proportion, setting up a one-tailed test at 2.5% level, using normal approximation to binomial, and solving for m from the critical region inequality. While it requires multiple steps and reverse-engineering the usual hypothesis test process, the techniques are all standard S1 content with no novel conceptual leaps required. |
| Spec | 2.04d Normal approximation to binomial2.05b Hypothesis test for binomial proportion |
| Total population | Number of children aged 5-17 |
| 56 075 912 | 8 473 617 |
The table shows information for England and Wales, taken from the UK 2011 census.
\begin{center}
\begin{tabular}{|l|c|}
\hline
Total population & Number of children aged 5-17 \\
\hline
56 075 912 & 8 473 617 \\
\hline
\end{tabular}
\end{center}
A random sample of 10 000 people in another country was chosen in 2011, and the number, $m$, of children aged 5-17 was noted.
It was found that there was evidence at the 2.5% level that the proportion of children aged 5-17 in the same year was higher than in the UK.
Unfortunately, when the results were recorded the value of $m$ was omitted.
Use an appropriate normal distribution to find an estimate of the smallest possible value of $m$. [5]
\hfill \mbox{\textit{OCR H240/02 2017 Q12 [5]}}