1 Gemma, a biologist, studies guillemots, which are a species of seabird. She has found that the weight of an adult guillemot may be modelled by a normal distribution with mean $\mu$ grams. During 2012, she measured the weight, $x$ grams, of each of a random sample of 9 adult guillemots and obtained the following results.

$$\sum x = 8532 \quad \text { and } \quad \sum ( x - \bar { x } ) ^ { 2 } = 38538$$
\begin{enumerate}[label=(\alph*)]
\item Construct a 98\% confidence interval for $\mu$ based on these data.
\item The corresponding confidence interval for $\mu$ obtained by Gemma based on a random sample of 9 adult guillemots measured during 2011 was $( 927,1063 )$, correct to the nearest gram.
\begin{enumerate}[label=(\roman*)]
\item Find the mean weight of guillemots in this sample.
\item Studies of some other species of seabird have suggested that their mean weights were less in 2012 than in 2011. Comment on whether Gemma's two confidence intervals provide evidence that the mean weight of guillemots was less in 2012 than in 2011.\\
(2 marks)
\end{enumerate}\end{enumerate}

\hfill \mbox{\textit{AQA S2 2013 Q1 [8]}}