# Question 4:

## Part (a):

| Answer/Working | Mark | Guidance |
|---|---|---|
| Attempt to rank depths against distances | M1 | For ranking attempt |
| $d$ values calculated from ranks | M1 | Must be using ranks |
| $\sum d^2 = 8$ | M1A1 | For sum of 8 (or 104 for reverse ranking) |
| $r_s = 1 - \frac{6 \times 8}{7 \times 48}$ | M1 | Correct formula with their $\sum d^2$; if answer not correct an expression is required |
| $= \frac{6}{7} = 0.857142...$ awrt **0.857** | A1 | Sign should correspond to ranking (use of 104 should get $-0.857$) |

## Part (b):

| Answer/Working | Mark | Guidance |
|---|---|---|
| $H_0: \rho = 0,\ H_1: \rho > 0$ | B1 | Both hypotheses in terms of $\rho$; $H_1$ must be one tail and compatible with ranking |
| Critical value at 1% level is 0.8929 | B1 | Accept $\pm$ |
| $r_s < 0.8929$ so not significant evidence to reject $H_0$ | M1 | Correct statement relating $r_s$ to cv; cv must satisfy $|cv|<1$ |
| The researcher's claim is not correct (at 1% level) / insufficient evidence for researcher's claim / insufficient evidence that water gets deeper further from inner bank | A1ft | Must mention "researcher" and "claim" or "distance (from bank)" and "depth (of water)"; use of "association" is A0 |

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