A researcher wishes to investigate the relationship between the amount of carbohydrate and the number of calories in different fruits. He compiles a list of 90 different fruits, e.g. apricots, kiwi fruits, raspberries.

As he does not have enough time to collect data for each of the 90 different fruits, he decides to select a simple random sample of 14 different fruits from the list. For each fruit selected, he then uses a dieting website to find the number of calories (kcal) and the amount of carbohydrate (g) in a typical adult portion (e.g. a whole apple, a bunch of 10 grapes, half a cup of strawberries). He enters these data into a spreadsheet for analysis.

\begin{enumerate}[label=(\alph*)]
\item Explain how the random number function on a calculator could be used to select this sample of 14 different fruits. [3]

\item The scatter graph represents 'Number of calories' against 'Carbohydrate' for the sample of 14 different fruits.

\begin{enumerate}[label=(\roman*)]
\item Describe the correlation between 'Number of calories' and 'Carbohydrate'. [1]

\item Interpret the correlation between 'Number of calories' and 'Carbohydrate' in this context. [1]
\end{enumerate}

\includegraphics{figure_1}

\item The equation of the regression line for this dataset is:

'Number of calories' = 12.4 + 2.9 × 'Carbohydrate'

\begin{enumerate}[label=(\roman*)]
\item Interpret the gradient of the regression line in this context. [1]

\item Explain why it is reasonable for the regression line to have a non-zero intercept in this context. [1]
\end{enumerate}
\end{enumerate}

\hfill \mbox{\textit{WJEC Unit 2  Q4 [7]}}