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=3.5Stating your hypotheses clearly and using a 5% level of significance, test the manufacturer's claim.
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'.
Practise Edexcel A Level Maths Hypothesis Testing with the Normal Distribution with exam-style questions for A Level Maths. 132 questions, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
