# Question 1:

## Part (a)

| Answer/Working | Marks | Guidance |
|---|---|---|
| Attempt to rank score $X$ and score $Y$ | M1 | For an attempt to rank both variables |
| Attempting $d^2$ for their ranks, must be using ranks | M1 | |
| $\sum d^2 = 18$ | A1 | For sum of 18 |
| $r_s = 1 - \frac{6 \times 18}{8(64-1)} = 0.7857...$ | M1A1 | awrt 0.786 |

**(5 marks)**

## Part (b)

| Answer/Working | Marks | Guidance |
|---|---|---|
| $H_0 : \rho = 0$ | B1 | Null hypothesis in terms of $\rho$ or $\rho_s$ |
| $H_1 : \rho > 0$ | B1 | Alt hypothesis as given |
| Critical region $r_s > 0.6429$ | B1 | cv of $+0.6429$ (or 0.7381 if two-tailed from hyp) |
| $(0.7857 > 0.6429)$ sufficient evidence to reject $H_0$ | M1 | Correct statement relating $r_s$ with cv, cv must be such that $\|cv\| < 1$ |
| There is evidence of agreement between the scores awarded by each manager | A1ft | Correct contextualised comment. Must mention "scores/rankings" and "manager". Use of "association" is A0 |

**(5 marks)**

## Part (c)

| Answer/Working | Marks | Guidance |
|---|---|---|
| ($A$ and $D$ are now) tied ranks (for Manager $Y$) | B1 | Tied ranks implied by 2.5, 6.5 or **both** 2 or 6 or description |
| Average rank awarded to $A$ and $D$, **and** use $r_s = \frac{S_{xy}}{\sqrt{S_{xx}S_{yy}}}$ | B1 | Average rank implied by 2.5 or 6.5 or description and 'use of pmcc' |

**(2 marks)**

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