| Exam Board | Edexcel |
|---|---|
| Module | S3 (Statistics 3) |
| Year | 2024 |
| Session | January |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Hypothesis test of Pearson’s product-moment correlation coefficient |
| Type | Two-tailed test for any correlation |
| Difficulty | Standard +0.3 This is a standard S3 hypothesis testing question requiring routine application of correlation coefficient formulas and critical value comparison. All necessary summary statistics are provided, eliminating computational difficulty. The question follows a textbook template with clearly signposted steps (calculate PMCC, perform test, calculate Spearman's, perform second test), requiring only procedural recall of standard techniques with no novel insight or problem-solving. |
| Spec | 5.08a Pearson correlation: calculate pmcc5.08d Hypothesis test: Pearson correlation5.08e Spearman rank correlation5.08f Hypothesis test: Spearman rank |
| Country | A | B | C | D | E | F | G |
| Annual tea consumption, \(\boldsymbol { t }\) (kg/person) | 0.27 | 0.15 | 0.42 | 0.06 | 1.94 | 0.78 | 0.44 |
| Population, \(\boldsymbol { p }\) (millions) | 5.4 | 5.8 | 9 | 10.2 | 67.9 | 17.1 | 8.7 |
\begin{enumerate}
\item The table shows the annual tea consumption, $t$ (kg/person), and population, $p$ (millions), for a random sample of 7 European countries.
\end{enumerate}
\begin{center}
\begin{tabular}{|l|l|l|l|l|l|l|l|}
\hline
Country & A & B & C & D & E & F & G \\
\hline
Annual tea consumption, $\boldsymbol { t }$ (kg/person) & 0.27 & 0.15 & 0.42 & 0.06 & 1.94 & 0.78 & 0.44 \\
\hline
Population, $\boldsymbol { p }$ (millions) & 5.4 & 5.8 & 9 & 10.2 & 67.9 & 17.1 & 8.7 \\
\hline
\end{tabular}
\end{center}
$$\text { (You may use } \mathrm { S } _ { t t } = 2.486 \quad \mathrm {~S} _ { p p } = 3026.234 \quad \mathrm {~S} _ { p t } = 83.634 \text { ) }$$
Angela suggests using the product moment correlation coefficient to calculate the correlation between annual tea consumption and population.\\
(a) Use Angela's suggestion to test, at the $5 \%$ level of significance, whether or not there is evidence of any correlation between annual tea consumption and population. State your hypotheses clearly and the critical value used.
Johan suggests using Spearman's rank correlation coefficient to calculate the correlation between the rank of annual tea consumption and the rank of population.\\
(b) Calculate Spearman's rank correlation coefficient between the rank of annual tea consumption and the rank of population.\\
(c) Use Johan's suggestion to test, at the $5 \%$ level of significance, whether or not there is evidence of a positive correlation between annual tea consumption and population.\\
State your hypotheses clearly and the critical value used.
\hfill \mbox{\textit{Edexcel S3 2024 Q3 [12]}}