| Exam Board | AQA |
|---|---|
| Module | S2 (Statistics 2) |
| Year | 2008 |
| Session | January |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Topic | T-tests (unknown variance) |
| Type | Single sample confidence interval t-distribution |
| Difficulty | Standard +0.3 This is a straightforward application of t-distribution confidence intervals with given summary statistics. Students must calculate sample mean and standard deviation from the given sums, then apply the standard t-interval formula. The 'hence comment' part requires minimal interpretation. While it's a multi-step question worth 8 marks total, it follows a completely standard template with no novel insight required, making it slightly easier than average for A-level. |
| Spec | 5.05c Hypothesis test: normal distribution for population mean5.05d Confidence intervals: using normal distribution |
4 A speed camera was used to measure the speed, $V$ mph, of John's serves during a tennis singles championship.
For 10 randomly selected serves,
$$\sum v = 1179 \quad \text { and } \quad \sum ( v - \bar { v } ) ^ { 2 } = 1014.9$$
where $\bar { v }$ is the sample mean.
\begin{enumerate}[label=(\alph*)]
\item Construct a $99 \%$ confidence interval for the mean speed of John's serves at this tennis championship, stating any assumption that you make.\\
(7 marks)
\item Hence comment on John's claim that, at this championship, he consistently served at speeds in excess of 130 mph .\\
(1 mark)
\end{enumerate}
\hfill \mbox{\textit{AQA S2 2008 Q4 [8]}}