# Question 4:

## Part (a)

| Answer/Working | Mark | Guidance |
|---|---|---|
| Ranks for $x$: 1,2,3,4,5,6,7,8,9,10 and $w$: 2,7,4,3,1,9,6,5,8,10 (or reversed) | M1 | Attempt to rank both $x$ and $w$; at least four correct |
| $\sum d^2 = 1+25+1+1+16+9+1+9+1+0 = 64$ | M1, A1 | Finding differences between ranks and evaluating $\sum d^2$; $\sum d^2 = 64$ |
| $r_s = 1 - \frac{6(64)}{10(99)}\ ; = 0.6121212...\ \left(\frac{101}{165}\right)$ | dM1; A1 | Using $1 - \frac{6\sum d^2}{10(99)}$ with their $\sum d^2$; awrt 0.612. Dependent on 1st M1. If $\sum d^2 = 266$, $r_s = \text{awrt}\ {-0.612}$: award M1M1A1M1A1 |

## Part (b)

| Answer/Working | Mark | Guidance |
|---|---|---|
| $H_0: \rho = 0$, $H_1: \rho > 0$ | B1 | Both hypotheses stated correctly in terms of $\rho$ |
| Critical value $r_s = 0.5636$ or CR: $r_s \geqslant 0.5636$ | B1 | |
| Since $r_s = 0.6121...$ lies in the CR; Result is significant; Reject $H_0$ | M1 | Correct statement relating their $r_s$ ($|r_s|<1$) with their c.v. where $|\text{c.v.}|<1$ |
| Conclude there is a positive correlation between systolic blood pressure and weight | A1 | Must mention "positive correlation", "blood pressure" and "weight". Follow through their $r_s$ with their c.v. (provided $|\text{c.v.}|<1$). Use of "association" is A0. Two-tailed test: max B0B1M1A0 |

## Part (c)

| Answer/Working | Mark | Guidance |
|---|---|---|
| Critical value $r = 0.5494$; CR: $r \geqslant 0.5494$; and since $r = 0.5114$ does not lie in CR; result is not significant; do not reject $H_0$ | M1 | |
| Conclude there is no positive correlation | A1 | Context not required |

## Part (d)

| Answer/Working | Mark | Guidance |
|---|---|---|
| "As $x$ increases, $w$ increases" **and** "the relationship is non-linear"; or "There is a positive correlation" **and** "the relationship is non-linear"; or "Data is not (bi-variate) normal" | B1 | Any one of these or equivalent |

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