## Part (i)
**Answer:**
Because if people cannot make a correct identification, then the probability that they guess correctly will be 0.5

For 'equally likely to guess right or wrong' or 'two outcomes with equal probability' or '50:50 chance of success' or 'right one in two occasions on average' or 'two (equally likely) outcomes' etc

**Marks:** E1 | E1 | [2]

**Guidance:**
- E1: For idea of a guess or 'chosen at random'
- E1: For idea of two outcomes. NB The question includes the sentence 'She suspects that people do no better than they would by guessing.', so this on its own does not get the mark for the idea of a guess

## Part (ii)
**Answer:**
'Because people may do better than they would by guessing' or similar

**Marks:** B1 | [1]

**Guidance:**
- B1: For idea of selecting correctly/identifying/knowing. No marks if answer implies that it is because there are over half in the sample who make a correct identification

## Part (iii)
**Answer:**
$$P(X \geq 13) = 1 - P(X \leq 12) = 1 - 0.8684 = 0.1316$$

NB PLEASE ANNOTATE THE TOP AND BOTTOM OF THE EXTRA PAGE IF NOT USED

$$0.1316 > 0.05$$

So not significant

There is insufficient evidence to suggest that people can make a correct identification.

**Marks:** M1 | B1* | M1* dep | A1* | E1* dep | [5]

**Guidance:**
- M1: For notation P(X ≥ 13) or P(X > 12) or 1– P(X ≤ 12)
- B1*: For 0.1316
- M1* dep: For comparison with 5%
- A1*: Allow 'accept H₀' or 'reject H₁'
- E1* dep: NB Point probabilities score zero. Must include 'insufficient evidence' or something similar such as 'to suggest that' ie an element of doubt either in the A or E mark. Must be in context to gain E1 mark. Do not allow 'sufficient evidence to suggest proportion making correct identification is 0.5' or similar

**ALTERNATIVE METHOD – follow method above unless some mention of CR seen**

**Critical region method**

UPPER TAIL

$$P(X \geq 14) = 1 - P(X \leq 13) = 1 - 0.9423 = 0.0577 > 5\%$$

$$P(X \geq 15) = 1 - P(X \leq 14) = 1 - 0.9793 = 0.0207 < 5\%$$

So critical region is {15,16,17,18,19,20}

13 not in CR so not significant

There is insufficient evidence to indicate that people can make a correct identification.

**Marks:** B1 | M1* | M1* cao dep on the two correct probabilities | A1* | E1* dep on A1 | [5]

**Guidance:**
- B1: For either probability
- M1*: For a correct comparison with 5%
- M1* cao dep: No marks if CR not justified. Condone {15, …, 20}, X ≥ 15, oe but not P(X ≥ 15,) etc
- A1*: Must include '13 not in CR'
- E1* dep: Ignore any work on lower critical region. NB If CR found correctly, then P(X=13) subsequently found, but cand says '13 not in CR' then allow up to all five marks. If do not say '13 not in CR' allow no marks

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