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'.
616 exam-style questions on Edexcel A Level Maths The Normal Distribution, covering 3.1 The Normal Distribution, 3.2 Finding Probabilities for Normal Distributions, 3.3 The Inverse Normal Distribution Function, 3.4 The Standard Normal Distribution, 3.5 Finding the mean and standard deviation, 3.6 Approximating a Binomial Distribution, and 3.7 Hypothesis Testing with the Normal Distribution. Each one has a worked solution and a mark scheme showing where the marks go.