| Exam Board | Edexcel |
|---|---|
| Module | S3 (Statistics 3) |
| Year | 2006 |
| Session | June |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Hypothesis test of Spearman’s rank correlation coefficien |
| Type | Hypothesis test for negative correlation |
| Difficulty | Standard +0.3 This is a standard textbook application of Spearman's rank correlation coefficient requiring ranking two variables, applying the formula (or calculating from ranks), and performing a routine hypothesis test with critical value lookup. While it involves multiple steps and careful arithmetic with 10 data points, it requires no problem-solving insight—just methodical application of a learned procedure. Slightly easier than average due to its purely procedural nature. |
| Spec | 5.08e Spearman rank correlation5.08f Hypothesis test: Spearman rank |
| Shop | Distance from tourist attraction (m) | Price (£) |
| A | 50 | 1.75 |
| B | 175 | 1.20 |
| C | 270 | 2.00 |
| D | 375 | 1.05 |
| E | 425 | 0.95 |
| F | 580 | 1.25 |
| G | 710 | 0.80 |
| H | 790 | 0.75 |
| I | 890 | 1.00 |
| J | 980 | 0.85 |
| Answer | Marks |
|---|---|
| Rank: | M1 |
| Answer | Marks | Guidance |
|---|---|---|
| \(r_s = 1 - \frac{6 \times 286}{10(10^2-1)} = -0.73\) or \(\frac{-11}{15}\) or \(-0.733\) | M1A1 | awrt 0.733 for either |
| Answer | Marks | Guidance |
|---|---|---|
| \(H_0: \rho = 0\) | B1 | |
| \(H_1: \rho < 0\) | B1 | (\(H_1: \rho > 0\) if rearrangement) |
| \(cv = -0.5636\) | B1 | (0.5636) |
| Reject \(H_0\), evidence there is a significant negative correlation between the price of an ice cream and the distance for a target location. | B1 | (ice cream get cheaper further from the target location) (-cv from correct table required) (positive in context) |
## Part (a)
Rank: | M1 |
Please verify a price, $\sum d^2 = 44$
$r_s = 1 - \frac{6 \times 286}{10(10^2-1)} = -0.73$ or $\frac{-11}{15}$ or $-0.733$ | M1A1 | awrt 0.733 for either
## Part (b)
$H_0: \rho = 0$ | B1 |
$H_1: \rho < 0$ | B1 | ($H_1: \rho > 0$ if rearrangement)
$cv = -0.5636$ | B1 | (0.5636)
Reject $H_0$, evidence there is a significant negative correlation between the price of an ice cream and the distance for a target location. | B1 | (ice cream get cheaper further from the target location) (-cv from correct table required) (positive in context)
---The table below shows the price of an ice cream and the distance of the shop where it was purchased from a particular tourist attraction.
\begin{center}
\begin{tabular}{|c|c|c|}
\hline
Shop & Distance from tourist attraction (m) & Price (£) \\
\hline
A & 50 & 1.75 \\
B & 175 & 1.20 \\
C & 270 & 2.00 \\
D & 375 & 1.05 \\
E & 425 & 0.95 \\
F & 580 & 1.25 \\
G & 710 & 0.80 \\
H & 790 & 0.75 \\
I & 890 & 1.00 \\
J & 980 & 0.85 \\
\hline
\end{tabular}
\end{center}
\begin{enumerate}[label=(\alph*)]
\item Find, to 3 decimal places, the Spearman rank correlation coefficient between the distance of the shop from the tourist attraction and the price of an ice cream. [5]
\item Stating your hypotheses clearly and using a 5\% one-tailed test, interpret your rank correlation coefficient. [4]
\end{enumerate}
\hfill \mbox{\textit{Edexcel S3 2006 Q4 [9]}}