# Question 1:

## Part (a)

| Answer/Working | Mark | Guidance |
|---|---|---|
| Ranks correctly assigned (Rank Age: 3,6,2,1,7,8,4,5 and Rank Breeder: 5,6,4,1,8,7,2,3) | M1 | Attempt to rank for actual ages or breeder's estimates. At least 4 correct in either row. Allow reverse rankings. |
| Finding differences between ranks and evaluating $\sum d^2$ | M1 | Independent of 1st M1 but must be ranks |
| $\sum d^2 = 4+0+4+0+1+1+4+4 = 18$ | A1 | |
| $r_s = 1 - \dfrac{6(18)}{8(8^2-1)}$ | dM1 | Dependent on 1st M1. For use of correct formula with their $\sum d^2$ |
| $\dfrac{11}{14}$ or awrt $0.786$ | A1 | |

**[5]**

## Part (b)

| Answer/Working | Mark | Guidance |
|---|---|---|
| $H_0: \rho = 0$, $H_1: \rho > 0$ | B1 | Both hypotheses correct in terms of $\rho$ or $\rho_s$ |
| Critical Value $= 0.8333$ or CR: $r_s \geqslant 0.8333$ | B1 | Critical value of $0.8333$ |
| Since $r_s = 0.7857...$ does not lie in the CR (or $0.7857... < 0.8333$), do not reject $H_0$ | M1 | For a correct statement relating their $r_s$ $(|r_s|<1)$ with their c.v. where $|\text{c.v.}|<1$ |
| The breeder does **not** have the ability to correctly order parrots by age / there is **insufficient evidence** that the breeder can correctly order parrots by age | A1ft | Must mention "breeder", "order", "parrots". All previous marks in part (b) must have been scored. |

**[4]**

**Note (Two-tailed test):** Applying a two-tailed test scores maximum B0B1M1A0. Award SC B0B1 for $H_0: \rho=0$, $H_1: \rho \neq 0$ followed by critical value $r_s = (\pm)0.881$ and allow access to M1 mark only.

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