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'.
209 exam-style questions on CCEA A Level Maths 4.6 Statistical hypothesis testing (A-level only), covering 4.6.1 Statistical hypothesis testing (A-level only), 4.6.2 Statistical hypothesis testing (A-level only), 4.6.3 Statistical hypothesis testing (A-level only), 4.6.4 Statistical hypothesis testing (A-level only), and 4.6.5 Statistical hypothesis testing (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.