| Exam Board | AQA |
|---|---|
| Module | S2 (Statistics 2) |
| Year | 2013 |
| Session | January |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Confidence intervals |
| Type | Unbiased estimates then CI |
| Difficulty | Standard +0.3 This is a straightforward hypothesis test for a normal mean with coded data. Students must decode to find sample mean (3018.47), calculate standard error, perform a two-tailed z-test, and identify error types. While it requires multiple steps and understanding of coding, it follows a standard S2 template with no conceptual surprises—slightly easier than average due to clear structure and routine application of formulas. |
| Spec | 5.05c Hypothesis test: normal distribution for population mean |
7 A factory produces 3-litre bottles of mineral water. The volume of water in a bottle has previously had a mean value of 3020 millilitres. Following a stoppage for maintenance, the volume of water, $x$ millilitres, in each of a random sample of 100 bottles is measured and the following data obtained, where $y = x - 3000$.
$$\sum y = 1847.0 \quad \sum ( y - \bar { y } ) ^ { 2 } = 6336.00$$
\begin{enumerate}[label=(\alph*)]
\item Carry out a hypothesis test, at the $5 \%$ significance level, to investigate whether the mean volume of water in a bottle has changed.\\
(8 marks)
\item Subsequent measurements establish that the mean volume of water in a bottle produced by the factory after the stoppage is 3020 millilitres. State whether a Type I error, a Type II error or no error was made when carrying out the test in part (a).\\
(l mark)
\end{enumerate}
\hfill \mbox{\textit{AQA S2 2013 Q7 [9]}}