A-LevelMathematicsProbability and statistics9709/62 · Feb/Mar 2024 · Q24 Marks

A random sample of 250 people living in Barapet was chosen. It was found that 78 of these people owned a BETEC phone.

(a)Calculate an approximate 98% confidence interval for the proportion of people living in Barapet who own a BETEC phone.[3]
(b)Manjit claims that more than 40% of the people living in Barapet own a BETEC phone. Use your answer to part (a) to comment on this claim.[1]

Mark scheme

Marking points from the official mark scheme (Feb/Mar 2024). The mark or mark type is shown in brackets.

[M1] (78 / 250) ± z * sqrt( (78 / 250) * (1 - 78 / 250) / 250 ) Use of a correct formula (any z).
[B1] z = 2.326
[A1] = 0.244 to 0.38[0] (3 sf) Must be an interval.
[B1] Unlikely to be true because confidence interval does not contain 0.4. FT their confidence interval. Must include this reason and 'unlikely', oe. Allow "not true because 0.4 is not in the confidence interval." But "Confidence interval only goes up to 0.38 so not true" and "'it' lies outside the confidence interval" both score B0.

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Topic: Probability and statistics, A-Level Mathematics (syllabus 9709). Structured question, 4 marks.
Source: A-Level Mathematics, Feb/Mar 2024 Paper 6 Variant 2, question 2.

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