VoltaicTech is developing a high-density electrolyte for their lithium-ion cells. They claim that this new formula increases the mean discharge lifespan of the batteries by more than 25 hours compared to the standard electrolyte. The population variance of the lifespan for the standard formula is known to be 144 hours2144 \text{ hours}^2144 hours2, while the population variance for the new formula is 256 hours2256 \text{ hours}^2256 hours2.
A random sample of 60 batteries using the standard formula resulted in a mean lifespan of 485 hours. A separate random sample of 100 batteries using the new formula resulted in a mean lifespan of 514 hours.
Stating your hypotheses clearly, test at the 1% level of significance whether or not there is evidence to support the claim that the mean lifespan with the new electrolyte is more than 25 hours greater than the mean lifespan with the standard electrolyte.
Explain the relevance of the Central Limit Theorem to the test conducted in part (a).
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.