A-LevelMathematicsProbability and statistics9709/61 · Oct/Nov 2024 · Q56 Marks

The lengths, in centimetres, of worms of a certain kind are normally distributed with mean μ and standard deviation 2.3. An article in a magazine states that the value of μ is 12.7 . A scientist wishes to test whether this value is correct. He measures the lengths, x cm, of a random sample of 50 worms of this kind and finds that Σx = 597.1 . He plans to carry out a test, at the 1% significance level, of whether the true value of μ is different from 12.7.

(a)State, with a reason, whether he should use a one-tailed or a two-tailed test.[1]
(b)Carry out the test.[5]

Mark scheme

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

[B1] Two-tailed because looking for difference
[B1] H₀: μ = 12.7 H₁: μ ≠ 12.7
[M1] (597.1/50 - 12.7) / (2.3 / √50)
[A1] = -2.330 Accept 2.336 or – 2.337
[M1] '-2.330' > -2.576 or '2.330' < 2.576 or '0.00989' > 0.005 or '0.0097' > 0.005
[A1 FT] [Not reject Ho] There is insufficient evidence to suggest that μ is not 12.7

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Topic: Probability and statistics, A-Level Mathematics (syllabus 9709). Structured question, 6 marks.
Source: A-Level Mathematics, Oct/Nov 2024 Paper 6 Variant 1, question 5.

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