# Question 6:

## Part (a):

| Answer/Working | Mark | Guidance |
|---|---|---|
| $H_0$: U[0,10] is a suitable model; $H_1$: U[0,10] is not a suitable model | B1 | |
| Values of $D$: correct intervals | B1 | For correct values of $D$ (can be implied by 40, 30, 20, 10) |
| Expected frequencies: 40, 30, 20, 10 | M1A1 | M1 for at least 2 expected frequencies or clear use of correct formula e.g. $0.4N$. A1 for all correct $E_i$ |
| $\frac{(O_i - E_i)^2}{E_i}$: 8.1, 2.7, 1.25, 1.6 | M1 | For at least 2 correct calculations from 4th or 5th column |
| $\chi^2 = 13.65$ | A1 | For test statistic of 13.65 (accept 13.7 to 3 sf). Awrt 13.7 only scores 2nd B1M1A1M1A1 |
| $\nu = 3$, $\chi^2_3(1\%) = 11.345$ | B1, B1 | |
| Reject $H_0$; the uniform distribution over [0,10] is not a suitable model | A1 | For correct conclusion rejecting uniform model, provided test statistic $> 11.345$ |

## Part (b):

| Answer/Working | Mark | Guidance |
|---|---|---|
| Area $\propto \pi r^2$ so $r = 81, -49 = \mathbf{32}$ | M1, A1 | M1 for some attempt to use $\pi r^2$ to find $r$ |
| $s = 100 - \text{"32"} - 49$ or $100 - 81 = \mathbf{19}$ | B1ft | |

## Part (c):

| Answer/Working | Mark | Guidance |
|---|---|---|
| Not significant, Henry's model is suitable | M1, A1 | M1 for correct statement that it is not significant. A1 for correctly stating Henry's model is suitable |

## Part (d):

| Answer/Working | Mark | Guidance |
|---|---|---|
| $H_0$: The colour/region chosen for the points is independent of gender (or no association) | B1 | Independence or association mentioned at least once. Allow connection but not correlation |
| $H_1$: The colour/region chosen for the points is dependent on gender (or association) | | |

## Part (e):

| Answer/Working | Mark | Guidance |
|---|---|---|
| $\frac{39 \times 65}{100}$ | B1 | |

## Part (f):

| Answer/Working | Mark | Guidance |
|---|---|---|
| Expected frequency for Yellow and Boys is $4.9 < 5$ so cells must be pooled/combined. This gives a $2 \times 3$ table so $\nu = (2-1)\times(3-1) = 2$ | B1 | For recognising there is an $E_i < 5$ and need for pooling/combining |

## Part (g):

| Answer/Working | Mark | Guidance |
|---|---|---|
| $\text{cv} = 4.605$ | B1 | |
| Not significant, so data do not support Phoebe's belief | B1 | For correctly stating Phoebe's belief is not supported (depends on their cv being $> 1.411$) |

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