AQA S1 2006 June — Question 1 8 marks

Exam BoardAQA
ModuleS1 (Statistics 1)
Year2006
SessionJune
Marks8
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicBivariate data
TypeCalculate r from raw bivariate data
DifficultyModerate -0.3 This is a standard S1 correlation calculation requiring systematic application of the PMCC formula with given data. While tedious with 8 data points, it involves only routine arithmetic and formula substitution with no conceptual challenges or problem-solving insight required. The interpretation parts are straightforward recall of correlation concepts.
Spec5.08a Pearson correlation: calculate pmcc5.08c Pearson: measure of straight-line fit

1 The table shows, for each of a random sample of 8 paperback fiction books, the number of pages, \(x\), and the recommended retail price, \(\pounds y\), to the nearest 10 p.
\(\boldsymbol { x }\)223276374433564612704766
\(\boldsymbol { y }\)6.504.005.508.004.505.008.005.50
    1. Calculate the value of the product moment correlation coefficient between \(x\) and \(y\).
    2. Interpret your value in the context of this question.
    3. Suggest one other variable, in addition to the number of pages, which may affect the recommended retail price of a paperback fiction book.
  1. The same 8 books were later included in a book sale. The value of the product moment correlation coefficient between the number of pages and the sale price was 0.959 , correct to three decimal places. What can be concluded from this value?

1 The table shows, for each of a random sample of 8 paperback fiction books, the number of pages, $x$, and the recommended retail price, $\pounds y$, to the nearest 10 p.

\begin{center}
\begin{tabular}{ | c | c | c | c | c | c | c | c | c | }
\hline
$\boldsymbol { x }$ & 223 & 276 & 374 & 433 & 564 & 612 & 704 & 766 \\
\hline
$\boldsymbol { y }$ & 6.50 & 4.00 & 5.50 & 8.00 & 4.50 & 5.00 & 8.00 & 5.50 \\
\hline
\end{tabular}
\end{center}
\begin{enumerate}[label=(\alph*)]
\item \begin{enumerate}[label=(\roman*)]
\item Calculate the value of the product moment correlation coefficient between $x$ and $y$.
\item Interpret your value in the context of this question.
\item Suggest one other variable, in addition to the number of pages, which may affect the recommended retail price of a paperback fiction book.
\end{enumerate}\item The same 8 books were later included in a book sale. The value of the product moment correlation coefficient between the number of pages and the sale price was 0.959 , correct to three decimal places.

What can be concluded from this value?
\end{enumerate}

\hfill \mbox{\textit{AQA S1 2006 Q1 [8]}}