| Exam Board | AQA |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2011 |
| Session | June |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Confidence intervals |
| Type | Calculate CI from summary stats |
| Difficulty | Moderate -0.3 This is a straightforward confidence interval question using t-distribution with standard bookwork calculations. Part (a) is pure arithmetic verification, part (b) requires routine application of the confidence interval formula, and part (c) asks for basic interpretation. While it involves multiple steps, each component is standard S1 material with no novel problem-solving required—slightly easier than average due to its predictable structure. |
| Spec | 5.05c Hypothesis test: normal distribution for population mean5.05d Confidence intervals: using normal distribution |
4 Rice that can be cooked in microwave ovens is sold in packets which the manufacturer claims contain a mean weight of more than 250 grams of rice.
The weight of rice in a packet may be modelled by a normal distribution.
A consumer organisation's researcher weighed the contents, $x$ grams, of each of a random sample of 50 packets. Her summarised results are:
$$\bar { x } = 251.1 \quad \text { and } \quad \sum ( x - \bar { x } ) ^ { 2 } = 184.5$$
\begin{enumerate}[label=(\alph*)]
\item Show that, correct to two decimal places, $s = 1.94$, where $s ^ { 2 }$ denotes the unbiased estimate of the population variance.
\item \begin{enumerate}[label=(\roman*)]
\item Construct a $96 \%$ confidence interval for the mean weight of rice in a packet, giving the limits to one decimal place.
\item Hence comment on the manufacturer's claim.
\end{enumerate}\item The statement '250 grams' is printed on each packet.
Explain, with reference to the values of $\bar { x }$ and $s$, why the consumer organisation may consider this statement to be dubious.
\end{enumerate}
\hfill \mbox{\textit{AQA S1 2011 Q4 [9]}}