# Question 1:

## Part (i)
| Answer | Marks | Guidance |
|--------|-------|----------|
| Attempt at ranking (allow all ranks reversed) | M1 | |
| $d^2$ values calculated | M1 | For $d^2$ |
| $\Sigma d^2 = 40$ | A1 | For 40 soi, e.g. can be implied by 0.242 seen |
| $r_s = 1 - \frac{6\Sigma d^2}{n(n^2-1)} = 1 - \frac{6\times40}{10\times99} = 1 - \frac{240}{990} = 1 - 0.242$ | M1 | For method for $r_s$ using their $\Sigma d^2$ |
| $= 0.758$ (to 3 s.f.) [allow 0.76 to 2 s.f.] | A1 | For 0.758 or 25/33 or 0.75 recurring; f.t. their $\Sigma d^2$ provided $|r_s| < 1$; Do not allow 0.7575; NB No ranking scores 0/5 |

## Part (ii)
| Answer | Marks | Guidance |
|--------|-------|----------|
| $H_0$: no association between diastolic blood pressure and systolic blood pressure in the population of young adults | B1 | Hypotheses must be in context; $H_0$: no association; $H_1$: positive association earns SC1; Hypotheses must **not** be given in terms of $\rho$; ignore references to $\rho$ if hypotheses also given in words |
| $H_1$: **positive** association between diastolic blood pressure and systolic blood pressure in the population of young adults | B1 | For **population of young adults** seen at least once; Do **not** allow **underlying population**; B0 for population correlation coefficient |
| One tail test critical value at 5% level is 0.5636 | B1* | For 0.5636; cv from pmcc test = 0.5494 gets B0 |
| Since $0.758 > 0.5636$, there is sufficient evidence to reject $H_0$ | M1dep* | For a sensible comparison leading to a conclusion of their $r_s$ with 0.5636, provided $0 < r_s < 1$; comparison may be in the form of a diagram |
| Conclude sufficient evidence to **suggest** positive association between diastolic and systolic blood pressure (in the population of young adults) | A1 | For **non-assertive**, correct conclusion in context; allow "support" in place of "suggest"; Do not allow "show", "imply", "conclude" or "prove"; If two-tailed test carried out award maxB1B0B1B1(for 0.6485)M0A0 |

## Part (iii)
| Answer | Marks | Guidance |
|--------|-------|----------|
| The scatter diagram does not appear to be roughly elliptical | E1 | For not elliptical; allow "not oval" |
| so the (population) may not have a bivariate Normal distribution | E1 | For not bivariate Normal; Do not allow "not Normal bivariate"; Do not allow "the **data** does not have a bivariate Normal distribution" |

## Part (iv)
| Answer | Marks | Guidance |
|--------|-------|----------|
| $H_0: \rho = 0$ | B1 | Do not allow other symbols unless clearly defined as population correlation coefficient; Do not allow hypotheses solely in words |
| $H_1: \rho > 0$ | | |
| where $\rho$ is the (population) correlation coefficient | B1 | For defining $\rho$ |
| For $n = 10$, 1% critical value $= 0.7155$ | B1* | For 0.7155 |
| Since $0.707 < 0.7155$ the result is not significant | M1dep* | For sensible comparison leading to a conclusion; conclusion soi |
| There is insufficient evidence at the 1% level to **suggest** that there is **positive** correlation between diastolic blood pressure and systolic blood pressure (in this population) | A1 | For **non-assertive** correct conclusion in context; If two-tailed test carried out award maxB0B1B1(for 0.7646)M0A0 |

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