| Exam Board | WJEC |
|---|---|
| Module | Further Unit 5 (Further Unit 5) |
| Session | Specimen |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Confidence intervals |
| Type | CI from raw data list |
| Difficulty | Standard +0.3 This is a standard confidence interval question using the t-distribution with small sample size. Part (a) requires routine calculation (mean, standard deviation, t-value lookup, CI formula) with no conceptual challenges. Part (b) tests understanding of CI interpretation, which is a common exam question. While it's Further Maths, this is basic statistical inference that's slightly easier than average A-level difficulty overall. |
| Spec | 5.05c Hypothesis test: normal distribution for population mean5.05d Confidence intervals: using normal distribution |
A factory manufactures a certain type of string. In order to ensure the quality of the product, a random sample of 10 pieces of string is taken every morning and the breaking strength of each piece, in Newtons, is measured. One morning, the results are as follows.
$$68.1 \quad 70.4 \quad 68.6 \quad 67.7 \quad 71.3 \quad 67.6 \quad 68.9 \quad 70.2 \quad 68.4 \quad 69.8$$
You may assume that this is a random sample from a normal distribution with unknown mean $\mu$ and unknown variance $\sigma^2$.
\begin{enumerate}[label=(\alph*)]
\item Determine a 95% confidence interval for $\mu$. [9]
\item The factory manager is given these results and he asks 'Can I assume that the confidence interval that you have given me contains $\mu$ with probability 0.95?' Explain why the answer to this question is no and give a correct interpretation. [2]
\end{enumerate}
\hfill \mbox{\textit{WJEC Further Unit 5 Q2 [11]}}