# Question 4:

## Part (a)
| Answer | Mark | Guidance |
|--------|------|----------|
| $H_0: p = 0.1 \quad H_1: p \neq 0.1$ [Allow 10% for 0.1] | B1 | Both hypotheses in terms of $p$ or $\pi$; must be attached to $H_0$ and $H_1$ |
| $[X \sim B(40, 0.1)] \Rightarrow P(X=0) = 0.0148$ [Allow any letter for $X$] | M1 | For use of correct model; implied by sight of at least one probability truncated or rounded to at least 2sf |
| $P(X \ldots 9) = 1 - P(X\ ,\ 8) = 1 - 0.9845 = 0.0155$ | A1 | For at least one correct probability (to at least 3sf) with its probability statement |
| Critical region is $\{X=0\} \cup \{X \ldots 9\}$ (o.e.) | A1 | For both correct probs and the correct critical region; allow $X < 1$ and $X > 8$ or words; allow ",", "or", "and", "or", "$\cap$" between $X\ ,\ 0$ and $X \ldots 9$ |

## Part (b)
| Answer | Mark | Guidance |
|--------|------|----------|
| $[\text{"0.0148"} + \text{"0.0155"}] = 0.0303$ | B1ft | For awrt 3.03% or correct sum of their two probabilities (provided each is less than 0.5); probabilities must be to at least 2sf and relate to their CR |

**Note:** To score in (c) they must have a CR of the form ($X = 0$ or $X < a$) and $X > b$, where $b$ is $\ldots 7$; may be implied by $P(X < a)$ and $P(X > b)$ i.e. 2nd A0 in (a) but correct form; need $b > a$

## Part (c)
| Answer | Mark | Guidance |
|--------|------|----------|
| [Provided 7 is not in their CR] insufficient evidence to support Freya's belief | B1 | For a suitable comment in context that suggests no support for Freya's belief/claim; or e.g. insufficient evidence of change in proportion/percentage of left-handed adults; or e.g. proportion/percentage of left-handed adults is not different from 10%; or e.g. 10% of adults in the country are left-handed; do not allow contradictory comments |

**NB:** A correct contextual answer in (c) using an acceptance region please send to review.

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