| Exam Board | Edexcel |
|---|---|
| Module | Paper 3 (Paper 3) |
| Session | Specimen |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Bivariate data |
| Type | Analyze large data set correlations |
| Difficulty | Moderate -0.3 This is a straightforward statistics question requiring interpretation of a scatter diagram, a routine hypothesis test for correlation (with critical value provided in tables), and knowledge recall about the large data set. The hypothesis test is standard bookwork, and the contextual parts require only basic familiarity with the dataset rather than mathematical problem-solving. |
| Spec | 2.01a Population and sample: terminology2.02c Scatter diagrams and regression lines2.02d Informal interpretation of correlation2.05f Pearson correlation coefficient2.05g Hypothesis test using Pearson's r |
| Answer | Marks | Guidance |
|---|---|---|
| Working/Answer | Mark | Guidance |
| Differentiate wrt \(t\) | M1 | At least one power going down |
| \(\mathbf{a} = (2t-3)\mathbf{i} - 12\mathbf{j}\) | A1 | A correct expression |
| \((2t-3)^2 + (-12)^2\) | M1 | Sum of squares of components (with or without square root) of a or F |
| \((2t-3)^2 + (-12)^2 = (6.5/0.5)^2\) | M1 | Equating magnitude to \(6.5/0.5\) or \(6.5\) as appropriate and squaring both sides |
| \(4t^2 - 12t - 16 = 0\) | A1 | Correct quadratic \(= 0\) in any form |
| \((t-4)(t+1) = 0\) | M1 | Attempt to solve a 3 term quadratic |
| \(t = 4\) | A1 | Correct answer |
## Question 2:
| Working/Answer | Mark | Guidance |
|---|---|---|
| Differentiate wrt $t$ | M1 | At least one power going down |
| $\mathbf{a} = (2t-3)\mathbf{i} - 12\mathbf{j}$ | A1 | A correct expression |
| $(2t-3)^2 + (-12)^2$ | M1 | Sum of squares of components (with or without square root) of **a** or **F** |
| $(2t-3)^2 + (-12)^2 = (6.5/0.5)^2$ | M1 | Equating magnitude to $6.5/0.5$ or $6.5$ as appropriate and squaring both sides |
| $4t^2 - 12t - 16 = 0$ | A1 | Correct quadratic $= 0$ in any form |
| $(t-4)(t+1) = 0$ | M1 | Attempt to solve a 3 term quadratic |
| $t = 4$ | A1 | Correct answer |
**Total: 7 marks**
---2. A researcher believes that there is a linear relationship between daily mean temperature and daily total rainfall. The 7 places in the northern hemisphere from the large data set are used. The mean of the daily mean temperatures, $t ^ { \circ } \mathrm { C }$, and the mean of the daily total rainfall, $s \mathrm {~mm}$, for the month of July in 2015 are shown on the scatter diagram below.\\
\includegraphics[max width=\textwidth, alt={}, center]{565bfa73-8095-4242-80b6-cd47aaff6a31-03_844_1339_497_372}
\begin{enumerate}[label=(\alph*)]
\item With reference to the scatter diagram, explain why a linear regression model may not be suitable for the relationship between $t$ and s .\\
(1)
The researcher calculated the product moment correlation coefficient for the 7 places and obtained $r = 0.658$.
\item Stating your hypotheses clearly, test at the $10 \%$ level of significance, whether or not the product moment correlation coefficient for the population is greater than zero.\\
(3)
\item Using your knowledge of the large data set, suggest the names of the 2 places labelled $G$ and $H$.\\
(1)
\item Using your knowledge from the large data set, and with reference to the locations of the two places labelled $G$ and $H$, give a reason why these places have the highest temperatures in July.\\
(2)
\item Suggest how you could make better use of the large data set to investigate the relationship between daily mean temperature and daily total rainfall.\\
(1)\\
(Total 7 marks)
\end{enumerate}
\hfill \mbox{\textit{Edexcel Paper 3 Q2 [7]}}