SPS SPS FM Statistics 2026 January — Question 3 8 marks

Exam BoardSPS
ModuleSPS FM Statistics (SPS FM Statistics)
Year2026
SessionJanuary
Marks8
TopicBivariate data
TypeCalculate r from summary statistics
DifficultyModerate -0.8 This is a straightforward application of the PMCC formula using given summary statistics, followed by a standard hypothesis test. Both are routine procedures covered in any A-level statistics course with no conceptual challenges or problem-solving required—just careful arithmetic and formula recall.
Spec2.05f Pearson correlation coefficient2.05g Hypothesis test using Pearson's r
3. A student is investigating the relationship between different electricity generation methods and cost of electricity in a particular country. The student first checks whether there is any correlation between the cost per unit of electricity, \(x\) euros, and the amount of electricity being generated by wind, \(y \mathrm { GW }\). The data from 30 observations are summarised as follows. \(n = 30 \quad \sum x = 2.219 \quad \sum y = 357.7 \quad \sum x ^ { 2 } = 0.2368 \quad \sum y ^ { 2 } = 4648 \quad \sum x y = 25.01\)
  1. In this question you must show detailed reasoning. Determine the product moment correlation coefficient.
  2. Carry out a hypothesis test at the \(5 \%\) level to investigate whether there is any correlation between the cost per unit of electricity and the amount of electricity generated by wind.
    [0pt] [4]
    [0pt]
3.

A student is investigating the relationship between different electricity generation methods and cost of electricity in a particular country. The student first checks whether there is any correlation between the cost per unit of electricity, $x$ euros, and the amount of electricity being generated by wind, $y \mathrm { GW }$. The data from 30 observations are summarised as follows.\\
$n = 30 \quad \sum x = 2.219 \quad \sum y = 357.7 \quad \sum x ^ { 2 } = 0.2368 \quad \sum y ^ { 2 } = 4648 \quad \sum x y = 25.01$
\begin{enumerate}[label=(\alph*)]
\item In this question you must show detailed reasoning.

Determine the product moment correlation coefficient.
\item Carry out a hypothesis test at the $5 \%$ level to investigate whether there is any correlation between the cost per unit of electricity and the amount of electricity generated by wind.\\[0pt]
[4]\\[0pt]

\end{enumerate}

\hfill \mbox{\textit{SPS SPS FM Statistics 2026 Q3 [8]}}
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