WJEC Unit 4 2018 June — Question 5 8 marks

Exam BoardWJEC
ModuleUnit 4 (Unit 4)
Year2018
SessionJune
Marks8
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TopicHypothesis test of Pearson’s product-moment correlation coefficient
TypeInterpret p-value for correlation test
DifficultyModerate -0.8 This is a straightforward hypothesis testing question on correlation requiring standard recall of the correlation test procedure and interpretation of p-values. Part (a) is simple interpretation of given statistics, part (b) follows a routine template (state hypotheses, compare r to critical value, conclude), and part (c) asks for basic understanding that both products being wheat-based suggests a common underlying factor. No complex calculations or novel insights required.
Spec2.05f Pearson correlation coefficient2.05g Hypothesis test using Pearson's r
Rebecca is a farmer who is monitoring prices for products to use on her farm. She records the prices of two products made from different grains, wheat and oats, at random points in time, to investigate whether there is any correlation. \includegraphics{figure_1} The product moment correlation coefficient for the data is \(0 \cdot 244\). There are 12 data points, and the \(p\)-value is \(0 \cdot 4447\).
  1. Comment on the correlation between the prices of Feed Wheat and Feed Oats. [2]
Rebecca also records the prices of two wheat products at random points in time, to investigate whether there is any correlation. \includegraphics{figure_2} The product moment correlation coefficient for the data is \(0 \cdot 653\). There are 12 data points.
  1. Stating your hypotheses clearly, test at the 5% level of significance whether there is any evidence of correlation between the prices of these two products. [5]
  2. Without referring to the positioning of the points on the graphs, suggest why the product moment correlation coefficient is higher for the second set of data. [1]
Rebecca is a farmer who is monitoring prices for products to use on her farm. She records the prices of two products made from different grains, wheat and oats, at random points in time, to investigate whether there is any correlation.

\includegraphics{figure_1}

The product moment correlation coefficient for the data is $0 \cdot 244$. There are 12 data points, and the $p$-value is $0 \cdot 4447$.

\begin{enumerate}[label=(\alph*)]
\item Comment on the correlation between the prices of Feed Wheat and Feed Oats. [2]
\end{enumerate}

Rebecca also records the prices of two wheat products at random points in time, to investigate whether there is any correlation.

\includegraphics{figure_2}

The product moment correlation coefficient for the data is $0 \cdot 653$. There are 12 data points.

\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Stating your hypotheses clearly, test at the 5% level of significance whether there is any evidence of correlation between the prices of these two products. [5]

\item Without referring to the positioning of the points on the graphs, suggest why the product moment correlation coefficient is higher for the second set of data. [1]
\end{enumerate}

\hfill \mbox{\textit{WJEC Unit 4 2018 Q5 [8]}}
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Q1 7 Q2 7 Q3 10 Q4 8 Q5 8 Q6 4 Q7 11 Q8 9 Q9 10 Q10 6