A-LevelMathematicsProbability and statistics9709/63 · May/June 2024 · Q45 Marks

In this question you should not use an approximating distribution. At an election in Menham last year, 24% of voters supported the Today Party. A student wishes to test whether support for the Today Party has decreased since last year. He chooses a random sample of 25 voters in Menham and finds that exactly 2 of them say that they support the Today Party. Test at the 5% significance level whether support for the Today Party has decreased.

Mark scheme

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

[B1] Ho: p = 0.24 H₁: p < 0.24
[M1] P(X≤2) = 0.76^25 + 25×0.76^24×0.24 + 25C2×0.76^23×0.24^2 or 0.0010479 + 0.0082732 + 0.0313513
[A1] = 0.0407
[M1] 0.0407 < 0.05
[A1FT] [Evidence to reject Ho.] There is sufficient evidence to suggest that the support for the Today Party has decreased.

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Topic: Probability and statistics, A-Level Mathematics (syllabus 9709). Structured question, 5 marks.
Source: A-Level Mathematics, May/June 2024 Paper 6 Variant 3, question 4.

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