A-LevelMathematicsProbability and statistics9709/61 · Oct/Nov 2025 · Q28 Marks

The mean mass of packets of Trueleaf tea is supposed to be 500 grams. An inspector wishes to test whether this value is correct. He weighs 60 randomly chosen packets and notes the mass, x grams, of each packet. The results are summarised as follows. n = 60 Σx = 29970 Σx² = 14970300

(a)Test, at the 5% significance level, whether the population mean mass is 500 grams.[8]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2025). The mark or mark type is shown in brackets.

B1
M1 Biased var = 4.75 M0.
A1
B1 Both. Not just ‘mean'.
M1 For standardising with their values. Must have ÷√60 . Ignore cc s.
A1 Allow -1.778 (from biased variance) accept 3 sf if nothing better.
M1 For valid comparison. Allow 1.778 < 1.96 0.0377 > 0.025.
A1FT In context. Not definite. No contradictions. FT from incorrect z. μ only accepted if defined. Accept CV method 499.5 > 499.44. Using biased var or using incorrect hypothesis can score a maximum of 6/8.

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Topic: Probability and statistics, A-Level Mathematics (syllabus 9709). Structured question, 8 marks.
Source: A-Level Mathematics, Oct/Nov 2025 Paper 6 Variant 1, question 2.

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