S1 June 2012 Q2
2. A bank reviews its customer records at the end of each month to find out how many customers have become unemployed, \(u\), and how many have had their house repossessed, \(h\), during that month. The bank codes the data using variables \(x = \dfrac{u - 100}{3}\) and \(y = \dfrac{h - 20}{7}\)
The results for the 12 months of 2009 are summarised below.
\[\sum x = 477 \quad S_{xx} = 5606.25 \quad \sum y = 480 \quad S_{yy} = 4244 \quad \sum xy = 23\,070\]The bank claims that an increase in unemployment among its customers is associated with an increase in house repossessions.
| Scheme | Marks |
|---|---|
| \(\left[S_{xy} =\right] 23070 - \dfrac{477\times 480}{12} \quad [= 3990]\) | B1 |
| \(r = \dfrac{\text{"}3990\text{"}}{\sqrt{5606.25\times 4244}}\) | M1 |
| \(= 0.81799\ldots\) awrt 0.818 | A1 |
| (3) |
Notes
Marks for part (a) must be seen in (a), do not award if only seen in (b)
B1 for a correct expression for \(S_{xy}\)
M1 for correct attempt at \(r\) f.t. their 3990 but \(\dfrac{23070}{\sqrt{5606.25\times 4244}}\) is M0
A1 for awrt 0.818 If an answer of 0.82 only is seen then B1M1A0 can be given
| Scheme | Marks |
|---|---|
| 0.818 | B1ft |
| (1) |
Notes
B1ft for awrt 0.818 or f.t. their answer to part (a) for \(|r| \lt 1\). Allow 2sf or 1sf follow through. Answer in (b) must be correct or match one of their answers in (a). Must be a number.
| Scheme | Marks |
|---|---|
| Positive correlation or value of \(r\) is close to 1 or value of \(r \gt 0\) (NOT “high/ strong correlation”) | B1 |
| So there is support for the bank’s claim or “increase in unemployment is accompanied by increase in house repossessions” | B1 |
| (2) | |
| (6 marks) |
Notes
1st B1 for a reason of positive correlation (allow even if \(r \gt 1\)). “positive skew” or “positive gradient” is B0 but 2nd B1 is still possible
2nd B1 for a comment that suggest this supports the claim. Marks in (c) are independent but first B1 requires some idea of positive correlation
(c) SC If \(|r| \lt 0.2\) allow this alternative to the mark scheme:
1st B1 for saying there is no or little correlation
2nd B1 for a comment that says this does not support the bank’s claim