## Question 6(i):

| Answer | Marks | Guidance |
|--------|-------|----------|
| $\text{mean} = 6.6$ | **B1** | **B1** for 6.6 (could be scored in iii) |
| $P(X \leqslant 1) = e^{-6.6}(1 + 6.6) = 0.0103$ | **M1** | Allow incorrect $\lambda$ in both probs |
| $P(X \leqslant 2) = e^{-6.6}(1 + 6.6 + \frac{6.6^2}{2}) = 0.0400$ | **M1A1** | **A1** for both values |
| CR is $X \leqslant 1$ | **DA1** | Dep on at least one **M** |
| $P(\text{Type I error}) = P(X \leqslant 1) = 0.0103$ | **B1FT** | FT their $P(X \leqslant 1)$ |
| **Total:** | **6** | |

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## Question 6(ii):

| Answer | Marks | Guidance |
|--------|-------|----------|
| Wrongly concluding that (mean) no of (sports) injuries has decreased | **B1** | Must be in context |
| **Total:** | **1** | |

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## Question 6(iii):

| Answer | Marks | Guidance |
|--------|-------|----------|
| $H_0: \lambda = 6.6 \quad H_1: \lambda < 6.6$ | **B1** | Can be scored in (i). Allow $\mu$ or $\lambda/1.1$ or 6.6 or $P(X \leqslant 2) = 0.0400 > 0.02$ |
| 2 not in CR | **M1** | |
| No evidence mean no. of injuries has decreased | **A1FT** | |
| **Total:** | **3** | |

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## Question 6(iv):

| Answer | Marks | Guidance |
|--------|-------|----------|
| $N(39.6,\ 39.6)$ | **B1** | May be implied |
| $\dfrac{29.5 - 39.6}{\sqrt{39.6}} = -1.605$ | **M1** | Allow with wrong or no cc |
| $\Phi(\text{"}-1.605\text{"}) = 1 - \Phi(\text{"1.605"})$ | **M1** | For area consistent with their mean |
| $= 0.0543$ (3 sfs) | **A1** | |
| **Total:** | **4** | |