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).