| Exam Board | Edexcel |
|---|---|
| Module | S3 (Statistics 3) |
| Marks | 10 |
| 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 pre-ranked data (no ties), followed by a standard hypothesis test using critical values from tables. The calculation is mechanical with 6 data points, and the interpretation is direct. Slightly above average difficulty only because it requires careful arithmetic and knowledge of the specific S3 test procedure, but involves no conceptual challenges or novel problem-solving. |
| Spec | 5.08e Spearman rank correlation5.08f Hypothesis test: Spearman rank |
| Answer | Marks | Guidance |
|---|---|---|
| Part (a) | M2 A1, M1 A1 | \(\sum d^2 = 22\); \(r_s = 1 - \frac{6 \times 22}{6 \times 35} = 0.3714\) |
| Part (b) | B1, M1 A1, A1 | \(H_0: \rho = 0\) \(H_1: \rho > 0\); \(n = 6\), 5% level \(\therefore\) C.R. is \(r_s > 0.8286\); \(0.3714 < 0.8286\) \(\therefore\) not significant; there is no evidence of positive correlation |
| Part (c) | B1, (10) | e.g. needs training as assessment not in line with experienced manager |
**Part (a)** | M2 A1, M1 A1 | $\sum d^2 = 22$; $r_s = 1 - \frac{6 \times 22}{6 \times 35} = 0.3714$
**Part (b)** | B1, M1 A1, A1 | $H_0: \rho = 0$ $H_1: \rho > 0$; $n = 6$, 5% level $\therefore$ C.R. is $r_s > 0.8286$; $0.3714 < 0.8286$ $\therefore$ not significant; there is no evidence of positive correlation
**Part (c)** | B1, (10) | e.g. needs training as assessment not in line with experienced managerA newly promoted manager is present when an experienced manager interviews six candidates, $A$, $B$, $C$, $D$, $E$ and $F$ for a job. Both managers rank the candidates in order of preference, starting with the best candidate, giving the following lists:
Experienced Manager: $B$ $F$ $A$ $C$ $E$ $D$
New Manager: $F$ $C$ $B$ $D$ $E$ $A$
\begin{enumerate}[label=(\alph*)]
\item Calculate Spearman's rank correlation coefficient for these data. [5]
\item Stating your hypotheses clearly, test at the 5\% level of significance whether or not there is evidence of positive correlation. [4]
\item Comment on whether the new manager needs training in the assessment of candidates at interview. [1]
\end{enumerate}
\hfill \mbox{\textit{Edexcel S3 Q3 [10]}}