| Exam Board | OCR |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2015 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Hypothesis test of Spearman’s rank correlation coefficien |
| Type | Calculate and interpret coefficient |
| Difficulty | Moderate -0.8 This is a straightforward application of Spearman's rank correlation formula with data already provided in rank order. The calculation is mechanical (computing d² values and applying the formula), and the interpretation requires only basic understanding that negative r_s indicates inverse relationship. No problem-solving insight needed, just routine procedure execution. |
| Spec | 5.08e Spearman rank correlation |
| Answer | Marks | Guidance |
|---|---|---|
| Quality: 1 3 4 2 5 6 8 7 9 | M1 | Attempt ranks; Y 80 83 81 82 84 85 87 86 88; Q1 2 3 4 5 6 7 8 9; A 1 4 2 3 5 6 8 7 9 |
| A1 | Correct ranks; Allow both sets of ranks reversed | |
| Attempt \(\Sigma d^2\) \((= 8)\) | M1 | |
| \(1 - \frac{6 \times 8}{9 \times (81-1)}\) | M1 | |
| \(= \frac{14}{15}\) or \(0.9\dot{3}\) or \(0.933\) (3 sf) | A1 | NB \(0.9\dot{3}\) is correct; One set reversed max 4 marks giving \(-\frac{14}{15}\) or \(-0.9\dot{3}\) or \(-0.933\) |
| Answer | Marks | Guidance |
|---|---|---|
| Older is better or newer is worse; As age increases, quality increases; Must imply older is better, ie "good (or positive) corr'n between age and quality" is not enough | B1 | No ft from (i); \(-0.933\) in (i) leads to same conclusion as \(+0.933\) in (ii); Nothing contradictory seen; NOT as year increases quality increases; NOT High/strong/good corr'n/agreement/rel'nship between age and quality |
# Question 3:
## Part (i)
Year: 80 81 82 83 84 85 86 87 88
Age: 1 2 3 4 5 6 7 8 9
Quality: 1 3 4 2 5 6 8 7 9 | M1 | Attempt ranks; Y 80 83 81 82 84 85 87 86 88; Q1 2 3 4 5 6 7 8 9; A 1 4 2 3 5 6 8 7 9
| A1 | Correct ranks; Allow both sets of ranks reversed
Attempt $\Sigma d^2$ $(= 8)$ | M1 |
$1 - \frac{6 \times 8}{9 \times (81-1)}$ | M1 |
$= \frac{14}{15}$ or $0.9\dot{3}$ or $0.933$ (3 sf) | A1 | NB $0.9\dot{3}$ is correct; One set reversed max 4 marks giving $-\frac{14}{15}$ or $-0.9\dot{3}$ or $-0.933$
**[5]**
## Part (ii)
Older is better or newer is worse; As age increases, quality increases; Must imply older is better, ie "good (or positive) corr'n between age and quality" is not enough | B1 | No ft from (i); $-0.933$ in (i) leads to same conclusion as $+0.933$ in (ii); Nothing contradictory seen; NOT as year increases quality increases; NOT High/strong/good corr'n/agreement/rel'nship between age and quality
**[1]**
---3 An expert tested the quality of the wines produced by a vineyard in 9 particular years. He placed them in the following order, starting with the best.
$$\begin{array} { l l l l l l l l l }
1980 & 1983 & 1981 & 1982 & 1984 & 1985 & 1987 & 1986 & 1988
\end{array}$$
(i) Calculate Spearman's rank correlation coefficient, $r _ { s }$, between the year of production and the quality of these wines. The years should be ranked from the earliest (1) to the latest (9).\\
(ii) State what this value of $r _ { s }$ shows in this context.
\hfill \mbox{\textit{OCR S1 2015 Q3 [6]}}