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A-LevelMathematicsProbability and statistics9709/61 · May/June 2020 · Q27 Marks

In the past the yield of a certain crop, in tonnes per hectare, had mean 0.56 and standard deviation 0.08. Following the introduction of a new fertilizer, the farmer intends to test at the 2.5% significance level whether the mean yield has increased. He finds that the mean yield over 10 years is 0.61 tonnes per hectare.

  1. (a)State two assumptions that are necessary for the test.[2]
  2. (b)Carry out the test.[5]

Mark scheme

Marking points from the official mark scheme (May/June 2020). The mark or mark type is shown in brackets.

  1. [B1] Assume standard deviation unchanged or standard deviation = 0.08
  2. [B1] Assume yields normally distributed
  3. [B1] Ho: Population mean yield (or μ) = 0.56
  4. [B1] H1: Population mean yield (or μ) > 0.56
  5. [M1] (0.61-0.56) / (0.08/√10)
  6. [A1] 1.976
  7. [M1] Comp 1.96
  8. [A1] There is evidence that mean yield has increased

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About this question

Topic
Probability and statistics, A-Level Mathematics (syllabus 9709). Structured question, 7 marks.
Source
A-Level Mathematics, May/June 2020 Paper 6 Variant 1, question 2.

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