S3 January 2006 Q7
7. The numbers of deaths from pneumoconiosis and lung cancer in a developing country are given in the table.
| Age group (years) | 20–29 | 30–39 | 40–49 | 50–59 | 60–69 | 70 and over |
|---|---|---|---|---|---|---|
| Deaths from pneumoconiosis (1000s) | 12.5 | 5.9 | 18.5 | 19.4 | 31.2 | 31.0 |
| Deaths from lung cancer (1000s) | 3.7 | 9.0 | 10.2 | 19.0 | 13.0 | 18.0 |
The correlation between the number of deaths in the different age groups for each disease is to be investigated.
(a) Give one reason why Spearman’s rank correlation coefficient should be used. (1)
(b) Calculate Spearman’s rank correlation coefficient for these data. (6)
(c) Use a suitable test, at the 5% significance level, to interpret your result. State your hypotheses clearly. (5)
| Scheme | Marks |
|---|---|
| The variables cannot be assumed to be normally distributed | B1 |
| (1) |
| Scheme | Marks | |||||||||||||||||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| M1 A1 dM1 (depends on ranking attempt) | |||||||||||||||||||||||||||||||||||
| \(\sum d^2 = 10\) (follow through their rankings) | A1 ft | |||||||||||||||||||||||||||||||||||
| \(r_s = 1 - \dfrac{6\sum d^2}{n(n^2 - 1)} = 1 - \dfrac{60}{210} = 0.714\) (\(\tfrac{5}{7}\) or awrt 0.714) | M1 A1 | |||||||||||||||||||||||||||||||||||
| (6) |
| Scheme | Marks |
|---|---|
| \(\mathrm{H}_0 : \rho = 0\) \(\mathrm{H}_1 : \rho \neq 0\) (or \(\rho \gt 0\)) | B1 B1 |
| \(n = 6 \Rightarrow\) 5% critical value = 0.8857 (or 0.8286) | B1ft |
| \(0.714 \lt 0.8857\) No evidence to reject \(\mathrm{H}_0\); | M1 |
| No evidence of correlation between deaths from pneumoconiosis and lung cancer. | A1 |
| (5) | |
| (12 marks) |