S3 June 2006 Q4
4. The table below shows the price of an ice cream and the distance of the shop where it was purchased from a particular tourist attraction.
| Shop | Distance from tourist attraction (m) | Price (£) |
|---|---|---|
| \(A\) | 50 | 1.75 |
| \(B\) | 175 | 1.20 |
| \(C\) | 270 | 2.00 |
| \(D\) | 375 | 1.05 |
| \(E\) | 425 | 0.95 |
| \(F\) | 580 | 1.25 |
| \(G\) | 710 | 0.80 |
| \(H\) | 790 | 0.75 |
| \(I\) | 890 | 1.00 |
| \(J\) | 980 | 0.85 |
(a) Find, to 3 decimal places, the Spearman rank correlation coefficient between the distance of the shop from the tourist attraction and the price of an ice cream. (5)
(b) Stating your hypotheses clearly and using a 5% one-tailed test, interpret your rank correlation coefficient. (4)
| Scheme | Marks | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Rank:
| M1 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
| \(\sum d^2 = 286\) Reverse ranking on price, \(\sum d^2 = 44\) | M1, A1 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
| \(r_s = 1 - \dfrac{6 \times 286}{10(100 - 1)} = -0.7\dot{3}\) or \(-\tfrac{11}{15}\) or awrt \(-0.733\) or awrt 0.733 for \(\sum d^2 = 44\) | M1 A1 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
| (5) |
| Scheme | Marks |
|---|---|
| \(\mathrm{H}_0 : \rho = 0\) | B1 |
| \(\mathrm{H}_1 : \rho \lt 0\) (\(\mathrm{H}_1 : \rho \gt 0\) if reverse ranking) | B1 |
| \(\text{cv} = -0.5636\) (0.5636) | B1 |
| Reject \(\mathrm{H}_0\), evidence that there is a significant negative correlation between the price of an ice cream and the distance from a tourist attraction. (Ice cream gets cheaper further from the tourist attraction) | B1 |
| (4) | |
| (9 marks) |
Notes
(−cv from correct table required) (positive in context)