# Question 1:

## Part (a)
| Answer | Mark | Guidance |
|--------|------|----------|
| Assign an average rank between the tied ranks | B1 | Must include reference to "average" rank; ignore comments about PMCC; do not allow "add 0.5 to both ranks" |

## Part (b)
| Answer | Mark | Guidance |
|--------|------|----------|
| Ranks for total tournaments: 1 3 4 6 8 9 2 5 10 7 | M1 | Attempt to rank total tournaments (at least four correct); condone reversed ranks |
| $\sum d^2 = 0+1+1+4+9+9+25+9+1+9 = 68$ | M1 | Finding differences between players rank and tournament ranks and evaluating $\sum d^2$; may be implied by 68 |
| $r_s = 1 - \dfrac{6 \times 68}{10(10^2-1)}$ | dM1 | Dependent on 1st M1; using $1 - \dfrac{6\sum d^2}{10(99)}$ with their $\sum d^2$; check $\sum d^2$ if no value shown |
| $= 0.5878\ldots$ awrt $0.588$ | A1 | Allow $\frac{97}{165}$ |

## Part (c)
| Answer | Mark | Guidance |
|--------|------|----------|
| $H_0: \rho = 0$, $H_1: \rho > 0$ | B1 | Both hypotheses correct; must be in terms of $\rho$; must be attached to $H_0$ and $H_1$; if $r_s$ is negative in (b) allow $H_1: \rho < 0$ |
| Critical Value $= 0.5636$ or CR $\ldots 0.5636$ | B1 | If $r_s$ is negative in (b) allow $-0.5636$ |
| Reject $H_0$ or significant or lies in the critical region | dM1 | Dependent on 2nd B1; correct statement consistent with their (b) and CV; no context needed but do not allow contradicting non-contextual comments |
| There is sufficient evidence of a positive correlation between rank and total tournaments won | A1 | Correct conclusion rejecting $H_0$; must mention **rank** and **total tournaments**; NB if $H_1: \rho < 0$ used, maximum B1B1dM1A0 |

## Part (d)
| Answer | Mark | Guidance |
|--------|------|----------|
| $2.5\%$ and $r_s = 0.6485$ or CR $\ldots 0.6485$ | B1 | For 2.5% and a correct critical value of 0.6485 |

---