| Exam Board | Edexcel |
|---|---|
| Module | FS2 (Further Statistics 2) |
| Year | 2024 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Hypothesis test of Spearman’s rank correlation coefficien |
| Type | Hypothesis test for positive correlation |
| Difficulty | Standard +0.3 This is a straightforward application of Spearman's rank correlation coefficient with clear data presentation. Students must calculate rs using the standard formula (requiring differences between ranks), then perform a one-tailed hypothesis test using critical value tables. While it's Further Maths content, the calculation is mechanical with no conceptual challenges—easier than average A-level questions overall. |
| Spec | 5.08e Spearman rank correlation5.08f Hypothesis test: Spearman rank |
| Rank | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| Customer 1 | \(A\) | \(E\) | \(C\) | \(F\) | \(G\) | \(B\) | \(D\) |
| Customer 2 | \(E\) | \(F\) | \(C\) | \(G\) | \(A\) | \(D\) | \(B\) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| Correct pairing of ranks (at least 4 pairs correct) | M1 | May be implied by a later calculation or awrt 0.571 |
| \(\sum d^2 = 16+1+1+1+1+4+1 = 24\) | M1 | Attempt at \(\sum d^2\) condoning slips; implied by 24 or awrt 0.571 |
| \(r_s = 1 - \frac{6 \times 24}{7(7^2-1)}\) | dM1 | Dependent on previous M; use of \(\sum d^2\) in correct formula (must be less than 112) |
| \(= 0.57142\ldots\) awrt \(0.571\) | A1 | awrt 0.571 with no incorrect working scores full marks; accept \(\frac{4}{7}\) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \(H_0: \rho_s = 0\), \(H_1: \rho_s > 0\) | B1 | Both hypotheses in terms of \(\rho\) or \(\rho_s\); do not allow \(r\) or \(r_s\) |
| 5% critical value \((\pm)\ 0.7143\) | B1 | Correct CV of \((\pm)\ 0.7143\) or better |
| Insufficient evidence to reject \(H_0\). There is no evidence to suggest the customers are in agreement | B1 | Correct conclusion based on cv and \(r_s\) such that \( |
## Question 2:
### Part (a):
| Answer/Working | Mark | Guidance |
|---|---|---|
| Correct pairing of ranks (at least 4 pairs correct) | M1 | May be implied by a later calculation or awrt 0.571 |
| $\sum d^2 = 16+1+1+1+1+4+1 = 24$ | M1 | Attempt at $\sum d^2$ condoning slips; implied by 24 or awrt 0.571 |
| $r_s = 1 - \frac{6 \times 24}{7(7^2-1)}$ | dM1 | Dependent on previous M; use of $\sum d^2$ in correct formula (must be less than 112) |
| $= 0.57142\ldots$ awrt $0.571$ | A1 | awrt 0.571 with no incorrect working scores full marks; accept $\frac{4}{7}$ |
### Part (b):
| Answer/Working | Mark | Guidance |
|---|---|---|
| $H_0: \rho_s = 0$, $H_1: \rho_s > 0$ | B1 | Both hypotheses in terms of $\rho$ or $\rho_s$; do not allow $r$ or $r_s$ |
| 5% critical value $(\pm)\ 0.7143$ | B1 | Correct CV of $(\pm)\ 0.7143$ or better |
| Insufficient evidence to reject $H_0$. There is no evidence to suggest the customers are in agreement | B1 | Correct conclusion based on cv and $r_s$ such that $|r_s| < |\text{CV}|$; suggesting insufficient evidence to suggest customers are in agreement; do NOT award if contradictory comments seen |
---\begin{enumerate}
\item An estate agent asks customers to rank 7 features of a house, $A , B , C , D , E , F$ and $G$, in order of importance. The responses for two randomly selected customers are in the table below.
\end{enumerate}
\begin{center}
\begin{tabular}{ | l | c | c | c | c | c | c | c | }
\hline
Rank & 1 & 2 & 3 & 4 & 5 & 6 & 7 \\
\hline
Customer 1 & $A$ & $E$ & $C$ & $F$ & $G$ & $B$ & $D$ \\
\hline
Customer 2 & $E$ & $F$ & $C$ & $G$ & $A$ & $D$ & $B$ \\
\hline
\end{tabular}
\end{center}
(a) Calculate Spearman's rank correlation coefficient for these data.\\
(b) Stating your hypotheses and critical value clearly, test at the $5 \%$ level of significance, whether or not the two customers are generally in agreement.
\hfill \mbox{\textit{Edexcel FS2 2024 Q2 [7]}}