| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9795/2 (Pre-U Further Mathematics Paper 2) |
| Year | 2017 |
| Session | June |
| Marks | 6 |
| Topic | Confidence intervals |
| Type | CI from raw data list |
| Difficulty | Standard +0.3 This is a straightforward confidence interval question requiring standard calculations from raw data (mean, standard deviation, t-distribution lookup) plus a definition. While it involves multiple steps, all are routine procedures covered in any statistics course with no conceptual challenges or novel problem-solving required. Slightly above average difficulty only due to the manual calculation burden and being Further Maths content. |
| Spec | 5.05d Confidence intervals: using normal distribution |
Total: 7 marks
**Part (i):**
On average 95% of all identically constructed confidence intervals contain the parameter. **B1**
Note: Use of "confident" without explanation: B0.
**Part (ii):**
$\bar{x} = 39.72$ **B1**
$s_{n-1} = 3.30711$ **B1** (3.31 or 10.9)
$39.72 \pm 2.776 \times \dfrac{3.30711}{\sqrt{5}}$ **M1** (Needs $\sqrt{5}$ but allow $s_n$, $z$, or FT errors)
All numbers correct (apart from $s_{n-1}$) soi **A1**
$= \text{awrt } (35.6, 43.8)$ **A1** Both correct to 3 SF. Condone wrong order.
Total: **7 marks**1 (i) Explain the meaning of the term ' $95 \%$ confidence interval'.\\
(ii) The values of five independent observations of a normally distributed random variable are as follows.
$$\begin{array} { l l l l l }
35.2 & 38.2 & 39.7 & 41.6 & 43.9
\end{array}$$
Obtain a 95\% confidence interval for the population mean.
\hfill \mbox{\textit{Pre-U Pre-U 9795/2 2017 Q1 [6]}}