A-LevelMathematicsProbability and statistics9709/63 · May/June 2022 · Q39 Marks

Batteries of type A are known to have a mean life of 150 hours. It is required to test whether a new type of battery, type B, has a shorter mean life than type A batteries.

(a)Give a reason for using a sample rather than the whole population in carrying out this test.[1]
(b)Test, at the 2% significance level, whether type B batteries have a shorter mean life than type A batteries.[5]
(c)Calculate a 94% confidence interval for the population mean life of type B batteries.[3]

Mark scheme

Marking points from the official mark scheme (May/June 2022). The mark or mark type is shown in brackets.

[B1] Batteries unusable after testing or Population too big or too costly or too time consuming to use the whole population oe
[B1] H₀: μ = 150, H₁: μ < 150
[M1] (147-150) / √(225/120)
[A1] -2.191
[M1] -2.191 < -2.054 [or –2.055]
[A1] [Reject H₀] There is evidence that the (mean) life of type B is less than type A (or less than 150)
[M1] 147 ± z x (15/√120)
[B1] z = 1.881 [or 1.882]
[A1] 144 to 150 (3 s.f.)

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About this question

Topic

Probability and statistics, A-Level Mathematics (syllabus 9709). Structured question, 9 marks.

Source

A-Level Mathematics, May/June 2022 Paper 6 Variant 3, question 3.

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