| Exam Board | AQA |
|---|---|
| Module | S2 (Statistics 2) |
| Year | 2013 |
| Session | January |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | 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 small sample size (n=6), requiring calculation of sample mean and standard deviation, then constructing a CI. Part (b) requires basic interpretation comparing the CI to a previous mean. The calculations are routine and the conceptual demand is modest—slightly easier than average since it's a standard textbook exercise with no novel problem-solving required. |
| Spec | 5.05d Confidence intervals: using normal distribution |
1 Dimitra is an athlete who competes in 400 m races. The times, in seconds, for her first six races of the 2012 season were
$$\begin{array} { l l l l l l }
54.86 & 53.09 & 53.75 & 52.88 & 51.97 & 51.81
\end{array}$$
\begin{enumerate}[label=(\alph*)]
\item Assuming that these data form a random sample from a normal distribution, construct a $95 \%$ confidence interval for the mean time of Dimitra's races in the 2012 season, giving the limits to two decimal places.
\item For the 2011 season, Dimitra's mean time for her races was 53.41 seconds. After her first six races of the 2012 season, her coach claimed that the data showed that she would be more successful in races during the 2012 season than during the 2011 season. Make two comments about the coach's claim.
\end{enumerate}
\hfill \mbox{\textit{AQA S2 2013 Q1 [7]}}