## Question 3:

### Part (a):

| | Senior Judge | Junior Judge | $d$ | $d^2$ |
|---|---|---|---|---|
| $A$ | 1 | 3 | -2 | 4 |
| $B$ | 2 | 1 | 1 | 1 |
| $C$ | 4 | 5 | -1 | 1 |
| $D$ | 3 | 2 | 1 | 1 |
| $E$ | 6 | 6 | 0 | 0 |
| $F$ | 5 | 4 | 1 | 1 |
| | | | | 8 |

M1 for attempt to rank judges' lists (at least 4 correct for each judge) | M1A1 | A1 for correct rankings for both (may be reversed); can be implied by correct $d^2$ or $r_s$; table could be ordered in terms of Senior Judge

$\sum d^2 = 8$ or 62 | A1 | 8 or 62 or correct $d^2$ row

$r_s = 1 - \frac{6 \times 8}{6 \times 35} = \frac{27}{35} = 0.771$ | dM1A1 | M1 for use of correct formula, follow through their $\sum d^2$ (dependent on 1st M1); if answer is not correct, a correct expression is required; A1 exact fraction or awrt $(\pm)0.771$

### Part (b):
$H_0: \rho = 0$ | B1 | Both hypotheses in terms of $\rho$ or $\rho_s$; hypotheses just in words e.g. "no correlation" score B0
$H_1: \rho > 0$ | |

Critical value $\pm 0.8286$ | B1 | Accept $\pm 0.8857$ if 2-tailed $H_1$

$(0.771 < 0.8286)$ so insufficient evidence to reject $H_0$ | M1 | Follow through from their $r_s$ and their c.v. if $|cv| < 1$ and $|r_s| < 1$

There is insufficient evidence to suggest a **positive** correlation between the judges | A1ft | A correct contextualised comment that includes "judges"

### Part (c):
For positive correlation c.v. is $0.8286 > 0.771$ | |

Training of junior judge was ineffective | B1ft | Follow through from their cv and $r_s$

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