# Question 2:

## Part (a):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $H_0: \rho = 0$, $H_1: \rho < 0$ | B1 | Both hypotheses in terms of $\rho$ |
| Critical value: $-0.6215$ (allow any cv in range $0.5 < |cv| < 0.75$) | M1 | Sight of $\pm 0.6215$ or any cv such that $0.5 < |cv| < 0.75$ |
| $r < -0.6215$ so significant result and there is evidence of a negative correlation between $w$ and $t$ | A1 | Must reject $H_0$ on basis of comparing $-0.915$ with $-0.6215$; must mention "negative", "correlation/relationship" and at least "$w$" and "$t$" |

## Part (b):
| Answer | Marks | Guidance |
|--------|-------|----------|
| e.g. As temperature increases people spend more time on the beach and less time shopping | B1 | Suitable reason to explain negative correlation using context. Mere description in context is B0. "Less clothes needed as temp increases" is B0 |

## Part (c):
| Answer | Marks | Guidance |
|--------|-------|----------|
| Since $r$ is close to $-1$, it is consistent with the suggestion | B1 | Suitable reason e.g. "strong"/"significant"/"near perfect" "correlation", $|r|$ close to 1, and saying it is consistent. Allow "yes" followed by reason |

## Part (d):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $t$ will be the explanatory variable since sales are likely to depend on the temperature | B1 | For identifying $t$ and giving suitable reason. Need idea that "$w$ depends on $t$" or "$w$ responds to $t$" or "$t$ affects $w$". Just saying "$t$ is the independent variable" or "$t$ explains change in $w$" is B0 |

## Part (e):
| Answer | Marks | Guidance |
|--------|-------|----------|
| Every degree rise in temperature leads to a drop in weekly earnings of £171 | B1 | Description conveying rate per degree Celsius. Must have 171, condone missing "£" sign |

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