| Exam Board | Edexcel |
|---|---|
| Module | Paper 3 (Paper 3) |
| Session | Specimen |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Bivariate data |
| Type | Analyze large data set correlations |
| Difficulty | Standard +0.3 This is a straightforward bivariate data question requiring standard statistical procedures: explaining extrapolation limitations, defining PMCC, performing a hypothesis test with given r-value, and interpreting summary statistics. All parts are routine textbook exercises with no novel problem-solving required, making it slightly easier than average. |
| Spec | 2.01a Population and sample: terminology2.05f Pearson correlation coefficient2.05g Hypothesis test using Pearson's r |
| \(\boldsymbol { t }\) | 13.3 | 16.2 | 15.7 | 16.6 | 16.3 | 16.4 | 19.3 | 17.1 | 13.2 |
| \(\boldsymbol { w }\) | 7 | 11 | 8 | 11 | 13 | 8 | 15 | 10 | 11 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| e.g. It requires extrapolation so will be unreliable | B1 | Correct statement with suitable reason |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| e.g. Linear association between \(w\) and \(t\) | B1 | Correct statement |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| \(H_0: \rho = 0 \quad H_1: \rho > 0\) | B1 | Both hypotheses in terms of \(\rho\) |
| Critical value 0.5822 | M1 | Selecting suitable 5% critical value compatible with their \(H_1\) |
| Reject \(H_0\); there is evidence that the product moment correlation coefficient is greater than 0 | A1 | Correct conclusion stated |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| Higher \(\bar{t}\) suggests overseas and not Perth; lower wind speed so perhaps not close to the sea so suggest Beijing | B1 | Suggest Beijing with supporting reason based on \(t\) or \(w\); allow Jacksonville with reason based on higher \(\bar{t}\) |
# Question 2:
## Part (a)
| Answer | Mark | Guidance |
|--------|------|----------|
| e.g. It requires extrapolation so will be unreliable | B1 | Correct statement with suitable reason |
## Part (b)
| Answer | Mark | Guidance |
|--------|------|----------|
| e.g. Linear association between $w$ and $t$ | B1 | Correct statement |
## Part (c)
| Answer | Mark | Guidance |
|--------|------|----------|
| $H_0: \rho = 0 \quad H_1: \rho > 0$ | B1 | Both hypotheses in terms of $\rho$ |
| Critical value 0.5822 | M1 | Selecting suitable 5% critical value compatible with their $H_1$ |
| Reject $H_0$; there is evidence that the product moment correlation coefficient is greater than 0 | A1 | Correct conclusion stated |
## Part (d)
| Answer | Mark | Guidance |
|--------|------|----------|
| Higher $\bar{t}$ suggests overseas and not Perth; lower wind speed so perhaps not close to the sea so suggest **Beijing** | B1 | Suggest Beijing with supporting reason based on $t$ or $w$; allow Jacksonville with reason based on higher $\bar{t}$ |
---\begin{enumerate}
\item A meteorologist believes that there is a relationship between the daily mean windspeed, $w \mathrm { kn }$, and the daily mean temperature, $t ^ { \circ } \mathrm { C }$. A random sample of 9 consecutive days is taken from past records from a town in the UK in July and the relevant data is given in the table below.
\end{enumerate}
\begin{center}
\begin{tabular}{ | c | c | c | c | c | c | c | c | c | c | }
\hline
$\boldsymbol { t }$ & 13.3 & 16.2 & 15.7 & 16.6 & 16.3 & 16.4 & 19.3 & 17.1 & 13.2 \\
\hline
$\boldsymbol { w }$ & 7 & 11 & 8 & 11 & 13 & 8 & 15 & 10 & 11 \\
\hline
\end{tabular}
\end{center}
The meteorologist calculated the product moment correlation coefficient for the 9 days and obtained $r = 0.609$\\
(a) Explain why a linear regression model based on these data is unreliable on a day when the mean temperature is $24 ^ { \circ } \mathrm { C }$\\
(b) State what is measured by the product moment correlation coefficient.\\
(c) Stating your hypotheses clearly test, at the $5 \%$ significance level, whether or not the product moment correlation coefficient for the population is greater than zero.
Using the same 9 days a location from the large data set gave $\bar { t } = 27.2$ and $\bar { w } = 3.5$\\
(d) Using your knowledge of the large data set, suggest, giving your reason, the location that gave rise to these statistics.
\hfill \mbox{\textit{Edexcel Paper 3 Q2 [6]}}