| Exam Board | OCR |
|---|---|
| Module | H240/02 (Pure Mathematics and Statistics) |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Topic | Z-tests (known variance) |
| Type | Test using proportion |
| Difficulty | Challenging +1.2 This is a reverse hypothesis test problem requiring students to work backwards from a significance level to find a critical value. While it involves multiple steps (calculating UK proportion, setting up normal approximation, finding critical z-value, solving for m), the techniques are all standard for A-level statistics: proportion hypothesis testing with normal approximation and using z-tables in reverse. The novelty of working backwards adds moderate difficulty beyond routine hypothesis test questions, but the mathematical demands remain straightforward. |
| Spec | 2.04d Normal approximation to binomial2.05b Hypothesis test for binomial proportion |
| Total population | Number of children aged 5-17 |
| 56075912 | 8473617 |
12 The table shows information for England and Wales, taken from the UK 2011 census.
\begin{center}
\begin{tabular}{ | c | c | }
\hline
Total population & Number of children aged 5-17 \\
\hline
56075912 & 8473617 \\
\hline
\end{tabular}
\end{center}
A random sample of 10000 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 $m$.
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\hfill \mbox{\textit{OCR H240/02 Q12 [5]}}