Skip to content

Course home

2.5.8 Hypothesis test for a single mean (A-level only)

2.5.8 Hypothesis test for a single mean (A-level only)

MediumHard
123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990
Question 40

The manufacturer of a specialized deep-sea sensor, the 'Hydra-X', claims that the mean operational lifespan of the unit exceeds 42 hours. A marine engineer monitors a random sample of 16 'Hydra-X' units to investigate this claim. The lifespan, T T\,T hours, of a unit is assumed to be normally distributed. The recorded sample statistics are:

xˉ=44.2,s=3.5 \bar{x} = 44.2, \quad s = 3.5 xˉ=44.2,s=3.5
a.

Stating your hypotheses clearly and using a 5% level of significance, test the manufacturer's claim.

[5]
b.

The standard deviation of the lifespan for the predecessor model, the 'Hydra-S', is 2.8 hours.

Stating your hypotheses clearly, test at the 5% level of significance whether there is evidence that the variance of the lifespan for the 'Hydra-X' is different from that of the 'Hydra-S'.

[5]
Markscheme

2.5.8 Hypothesis test for a single mean (A-level only) Questions

  1. A Level
  2. /Maths
  3. /2.5.8 Hypothesis test for a single mean (A-level only)

132 exam-style questions on OCR (MEI) A Level Maths 2.5.8 Hypothesis test for a single mean (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

Question bank