| Exam Board | OCR |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2014 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Hypothesis test of Spearman’s rank correlation coefficien |
| Type | Determine ranks from coefficient |
| Difficulty | Moderate -0.8 This question tests basic understanding of Spearman's rank correlation coefficient through straightforward applications. Part (i) requires recognizing that rs = -1 means perfect negative correlation (ranks are reversed: 6,5,4,3,2,1), which is direct recall. Part (ii) involves a simple calculation using the standard formula with given rank differences. Both parts are routine exercises with no problem-solving or conceptual challenges beyond knowing the definition and formula. |
| Spec | 5.08e Spearman rank correlation5.08f Hypothesis test: Spearman rank |
| Team | A | B | C | D | E | F |
| Number of goals FOR (rank) | 1 | 2 | 3 | 4 | 5 | 6 |
| Number of goals AGAINST (rank) |
| Team | G | H |
| Number of goals scored (rank) | 7 | 8 |
| Number of points gained (rank) | 8 | 7 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| 6 5 4 3 2 1 | B1 | |
| [1] |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(\Sigma d^2 = 0\) for first 6 teams | M1 | May be implied by use of \(\Sigma d^2 = 2\) |
| \(\Sigma d^2 = 2\) | B1 | |
| \(1 - \frac{6\Sigma d^2}{8(8^2-1)}\) | M1 | ft their \(\Sigma d^2\) \((\neq 0)\) — using ranks from (i) can score 2nd M1 only |
| \(= \frac{41}{42}\) or \(0.976\) (3 sf) | A1 | |
| [4] |
# Question 6:
## Part 6(i):
| Answer | Marks | Guidance |
|--------|-------|----------|
| 6 5 4 3 2 1 | B1 | |
| **[1]** | | |
## Part 6(ii):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $\Sigma d^2 = 0$ for first 6 teams | M1 | May be implied by use of $\Sigma d^2 = 2$ |
| $\Sigma d^2 = 2$ | B1 | |
| $1 - \frac{6\Sigma d^2}{8(8^2-1)}$ | M1 | ft their $\Sigma d^2$ $(\neq 0)$ — using ranks from (i) can score 2nd M1 only |
| $= \frac{41}{42}$ or $0.976$ (3 sf) | A1 | |
| **[4]** | | |
---6 Fiona and James collected the results for six hockey teams at the end of the season. They then carried out various calculations using Spearman's rank correlation coefficient, $r _ { s }$.\\
(i) Fiona calculated the value of $r _ { s }$ between the number of goals scored FOR each team and the number of goals scored AGAINST each team. She found that $r _ { s } = - 1$. Complete the table in the answer book showing the ranks.
\begin{center}
\begin{tabular}{ | l | c | c | c | c | c | c | }
\hline
Team & A & B & C & D & E & F \\
\hline
Number of goals FOR (rank) & 1 & 2 & 3 & 4 & 5 & 6 \\
\hline
Number of goals AGAINST (rank) & & & & & & \\
\hline
\end{tabular}
\end{center}
(ii) James calculated the value of $r _ { s }$ between the number of goals scored and the number of points gained by the 6 teams. He found the value of $r _ { s }$ to be 1 . He then decided to include the results of another two teams in the calculation of $r _ { s }$. The table shows the ranks for these two teams.
\begin{center}
\begin{tabular}{ | l | c | c | }
\hline
Team & G & H \\
\hline
Number of goals scored (rank) & 7 & 8 \\
\hline
Number of points gained (rank) & 8 & 7 \\
\hline
\end{tabular}
\end{center}
Calculate the value of $r _ { s }$ for all 8 teams.
\hfill \mbox{\textit{OCR S1 2014 Q6 [5]}}