| Exam Board | AQA |
|---|---|
| Module | S2 (Statistics 2) |
| Year | 2006 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | T-tests (unknown variance) |
| Type | Single sample confidence interval t-distribution |
| Difficulty | Moderate -0.3 This is a straightforward application of t-distribution confidence intervals with small sample size. Part (a) requires standard calculation of sample mean, sample standard deviation, and applying the t-interval formula—routine for S2 students. Part (b) tests understanding of confidence interval interpretation (answer is simply 0.05), which is conceptual but basic. Slightly easier than average due to minimal computational complexity and no problem-solving insight required. |
| Spec | 5.05d Confidence intervals: using normal distribution |
| Answer | Marks | Guidance |
|---|---|---|
| \(\bar{x} = \frac{254}{5} = 50.8\) | B1 | |
| \(s = 4.55\) | B1 | |
| \(v = 5 - 1 = 4\) | B1 | |
| \(t_{\text{crit}} = 2.776\) | B1 | |
| \(95\%\) confidence interval \(= 50.8 \pm 2.776 \times \frac{4.55}{\sqrt{5}}\) | M1 | ft their values |
| \(= 50.8 \pm 5.648\) | ||
| \(= (45.2, 56.4)\) | A1 |
| Answer | Marks |
|---|---|
| \(0.05\) | B1 |
## 2(a)
$\bar{x} = \frac{254}{5} = 50.8$ | B1 |
$s = 4.55$ | B1 |
$v = 5 - 1 = 4$ | B1 |
$t_{\text{crit}} = 2.776$ | B1 |
$95\%$ confidence interval $= 50.8 \pm 2.776 \times \frac{4.55}{\sqrt{5}}$ | M1 | ft their values
$= 50.8 \pm 5.648$ |
$= (45.2, 56.4)$ | A1 |
## 2(b)
$0.05$ | B1 |
---2 The weights of lions kept in captivity at Wildcat Safari Park are normally distributed.\\
The weights, in kilograms, of a random sample of five lions were recorded as
$$\begin{array} { l l l l l }
46 & 48 & 57 & 49 & 54
\end{array}$$
\begin{enumerate}[label=(\alph*)]
\item Construct a 95\% confidence interval for the mean weight of lions kept in captivity at Wildcat Safari Park.
\item State the probability that this confidence interval does not contain the mean weight of lions kept in captivity at Wildcat Safari Park.
\end{enumerate}
\hfill \mbox{\textit{AQA S2 2006 Q2 [7]}}