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A company has designed a new ink-jet cartridge for its plain-paper printers which it believes has a longer average lifetime than the one currently being produced. The historical average lifetime for the cartridges currently produced has been 1502 pages. To test whether the new product has a longer lifetime, they take a sample of 24 of the new cartridges by counting the number of high-quality printed pages each was able to produce and found a mean of 1511.4 pages and a standard deviation of 35.7 pages.
a) Formulate and conduct an appropriate hypothesis test to determine whether the new cartridges have a longer average lifetime than the current product, where the maximum risk of rejecting a true hypothesis is 0.01.
b) What is the recommended action by the printer company?
c) What assumption(s) are necessary to conduct the test in part (a)?
d) What is the probability of a type I error for the test in part (a)?
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