# Question 2:

## Part (a):

| Answer/Working | Mark | Guidance |
|---|---|---|
| Attempt to rank Aarush's order and actual order (ranks as shown in table) | M1 | At least 4 correct in either row |
| $\sum d^2 = 1+1+1+1+4+1+1 = 10$ | M1 | Finding differences between each pair of ranks and evaluating $\sum d^2$ |
| $r_s = 1 - \dfrac{6 \times 10}{7 \times 48}$ | dM1 | Dependent on previous 2 M marks; using $r_s = 1 - \dfrac{6\sum d^2}{7\times 48}$ |
| $= 0.8214...$ awrt $0.821$ | A1cso | Allow $\dfrac{23}{28}$ |

## Part (b):

| Answer/Working | Mark | Guidance |
|---|---|---|
| $H_0: \rho = 0$, $H_1: \rho > 0$ | B1 | Both hypotheses in terms of $\rho$ or $\rho_s$; condone $p$; cannot use $r$ |
| Critical value $r_s = 0.7143$ | M1 | Allow $|$CV$| = 0.7143$ or better |
| Reject $H_0$ / result is significant / $r_s$ lies in critical region | M1 | Correct non-contradictory statement consistent with $r_s < 1$ and CV |
| Evidence to support Aarush can **rank** the **kettles** in order of **price** | A1 | Dependent on all previous method marks; must reject $H_0$; needs **rank**, **kettles**, **price** |

## Part (c):

| Answer/Working | Mark | Guidance |
|---|---|---|
| Aarush has already ranked them, or the order/price is not normally distributed | B1 | Correct reason; data already ranked; condone "it is ordinal data" |

## Part (d):

| Answer/Working | Mark | Guidance |
|---|---|---|
| Kettles $A$ and $D$ would have a tied rank $(1.5)$ | B1 | Must mention both $A$ and $D$; allow "equal rank", "average rank"; condone "order" for rank |

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