| Exam Board | AQA |
|---|---|
| Module | S2 (Statistics 2) |
| Year | 2014 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Confidence intervals |
| Type | CI from raw data list |
| Difficulty | Moderate -0.3 Part (a) is a standard confidence interval calculation for a normal distribution with unknown variance (t-distribution), requiring routine computation of mean, standard deviation, and application of the formula. Part (b) tests basic understanding of confidence interval interpretation (expecting 10% of 30 intervals to miss μ). While multi-step, this is a textbook exercise with no novel insight required, making it slightly easier than average. |
| Spec | 5.05d Confidence intervals: using normal distribution |
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Please provide the mark scheme text you'd like me to clean up, and I'll convert the unicode symbols to LaTeX notation and format it according to your specifications.1 Vanya collected five samples of air and measured the carbon dioxide content of each sample, in parts per million by volume (ppmv). The results were as follows.
$$\begin{array} { l l l l l }
387 & 375 & 382 & 379 & 381
\end{array}$$
\begin{enumerate}[label=(\alph*)]
\item Assuming that these data form a random sample from a normal distribution with mean $\mu$ ppmv, construct a $90 \%$ confidence interval for $\mu$.\\[0pt]
[6 marks]
\item Vanya repeated her sampling procedure on each of 30 days and, for each day's results, a $90 \%$ confidence interval for $\mu$ was constructed.
On how many of these 30 days would you expect $\mu$ to lie outside that day's confidence interval?\\[0pt]
[1 mark]
\end{enumerate}
\hfill \mbox{\textit{AQA S2 2014 Q1 [7]}}