| Exam Board | Edexcel |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2008 |
| Session | January |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Bivariate data |
| Type | Calculate Spearman's rank correlation |
| Difficulty | Moderate -0.3 This is a standard S1 correlation calculation requiring the PMCC formula with given summary statistics, followed by straightforward interpretation. The arithmetic is routine and the context interpretation is basic (comparing two correlation values). Slightly easier than average due to provided summaries and no ranking complications. |
| Spec | 5.08a Pearson correlation: calculate pmcc5.08d Hypothesis test: Pearson correlation5.09e Use regression: for estimation in context |
| Employee | A | \(B\) | C | D | \(E\) | \(F\) | G | \(H\) | I | J |
| Interview test, \(x\) \%. | 65 | 71 | 79 | 77 | 85 | 78 | 85 | 90 | 81 | 62 |
| Performance after one year, \(y \%\). | 65 | 74 | 82 | 64 | 87 | 78 | 61 | 65 | 79 | 69 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(\sum x = 773\), \(\sum y = 724\) | B1, B1 | Both sums must be seen or implied |
| \(r = \frac{10 \times 56076 - 773 \times 724}{\sqrt{(10 \times 60475 - 773^2)(10 \times 53122 - 724^2)}}\) | M1, A1ft | M1 for at least one correct attempt at \(S_{xx}\), \(S_{yy}\) or \(S_{xy}\) and using correct formula; A1ft for fully correct expression |
| \(r = 0.155357...\) | A1 | A1 for awrt 0.155 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| Both weak correlation | B1g | |
| Neither score is a good indication of future performance | B1h | If \( |
| Interview test is slightly better since correlation is positive | Third line for comment distinguishing tests |
## Question 1:
### Part (a)
| Answer/Working | Marks | Guidance |
|---|---|---|
| $\sum x = 773$, $\sum y = 724$ | B1, B1 | Both sums must be seen or implied |
| $r = \frac{10 \times 56076 - 773 \times 724}{\sqrt{(10 \times 60475 - 773^2)(10 \times 53122 - 724^2)}}$ | M1, A1ft | M1 for at least one correct attempt at $S_{xx}$, $S_{yy}$ or $S_{xy}$ and using correct formula; A1ft for fully correct expression |
| $r = 0.155357...$ | A1 | A1 for awrt 0.155 |
**NB:** $S_{xx} = 722.1$, $S_{yy} = 704.4$, $S_{xy} = 110.8$
### Part (b)
| Answer/Working | Marks | Guidance |
|---|---|---|
| Both weak correlation | B1g | |
| Neither score is a good indication of future performance | B1h | If $|r| > 0.5$: B1g possible but B0h |
| Interview test is slightly better since correlation is positive | | Third line for comment distinguishing tests |
---\begin{enumerate}
\item A personnel manager wants to find out if a test carried out during an employee's interview and a skills assessment at the end of basic training is a guide to performance after working for the company for one year.
\end{enumerate}
The table below shows the results of the interview test of 10 employees and their performance after one year.
\begin{center}
\begin{tabular}{|l|l|l|l|l|l|l|l|l|l|l|}
\hline
Employee & A & $B$ & C & D & $E$ & $F$ & G & $H$ & I & J \\
\hline
Interview test, $x$ \%. & 65 & 71 & 79 & 77 & 85 & 78 & 85 & 90 & 81 & 62 \\
\hline
Performance after one year, $y \%$. & 65 & 74 & 82 & 64 & 87 & 78 & 61 & 65 & 79 & 69 \\
\hline
\end{tabular}
\end{center}
$$\text { [You may use } \sum x ^ { 2 } = 60475 , \sum y ^ { 2 } = 53122 , \sum x y = 56076 \text { ] }$$
(a) Showing your working clearly, calculate the product moment correlation coefficient between the interview test and the performance after one year.
The product moment correlation coefficient between the skills assessment and the performance after one year is - 0.156 to 3 significant figures.\\
(b) Use your answer to part (a) to comment on whether or not the interview test and skills assessment are a guide to the performance after one year. Give clear reasons for your answers.
\hfill \mbox{\textit{Edexcel S1 2008 Q1 [7]}}