| Exam Board | WJEC |
|---|---|
| Module | Further Unit 5 (Further Unit 5) |
| Year | 2024 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Confidence intervals |
| Type | Calculate CI for proportion |
| Difficulty | Moderate -0.8 This is a straightforward confidence interval question requiring standard formula application: calculating p-hat (55/80), finding the standard error, and using z=1.645 for 90% CI. Part (b) is trivial (50×0.9=45). Despite being Further Maths, this is routine statistical inference with no conceptual challenges or novel problem-solving required. |
| Spec | 2.05b Hypothesis test for binomial proportion |
Tony runs a pie stand that sells two types of pie outside a football ground. He wants to estimate the probability that a customer will buy a steak pie rather than a vegetable pie. He conducts a survey by randomly selecting customers and recording their choice of pie. When he feels he has enough data, he notes that 55 customers bought steak pies and 25 bought vegetable pies.
\begin{enumerate}[label=(\alph*)]
\item Calculate an approximate 90\% confidence interval for $p$, the probability that a randomly selected customer buys a steak pie. [6]
\item Suppose that Tony carries out 50 such surveys and calculates 90\% confidence intervals for each survey. Determine the expected number of these confidence intervals that would contain the true value of $p$. [1]
\end{enumerate}
\hfill \mbox{\textit{WJEC Further Unit 5 2024 Q3 [7]}}