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).
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