Volt-Tech is testing a next-generation solar storage unit, the "Cell-X", as a potential replacement for their existing "Cell-S" model. Engineers want to determine if the mean storage capacity of the Cell-X unit is more than 2.5 kWh greater than that of the Cell-S unit. The variance in capacity for the Cell-S is known to be 1.0 kWh2, and for the Cell-X, it is 2.0 kWh2.
A random sample of 50 Cell-S units was found to have a mean capacity of 42.4 kWh. A random sample of 100 Cell-X units was found to have a mean capacity of 45.6 kWh.
Stating your hypotheses clearly, test at the 1% level of significance whether there is evidence that the mean capacity of the Cell-X units is more than 2.5 kWh greater than the mean capacity of the Cell-S units.
Explain the relevance of the Central Limit Theorem to the test conducted in part (a).
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.