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'.
316 exam-style questions on OCR A Level Maths 2.5 Statistical Hypothesis Testing, covering 2.5.1 The language of hypothesis testing, 2.5.2 Hypothesis test for a binomial proportion, 2.5.3 Inference and significance level, 2.5.4 Sample mean as a random variable (A-level only), 2.5.5 Hypothesis test for the mean of a normal distribution (A-level only), 2.5.6 Pearson's product-moment correlation coefficient, and 2.5.7 Hypothesis test using Pearson's coefficient (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.