A company has devised a new ink-jet cartridge for its plain-paper fax machine that it believes has a longer lifetime (on average) than the one currently being produced. To investigate its length of life, 225 of the new cartridges were tested by counting the number of highquality printed pages each was able to produce. The sample mean and standard deviation were determined to be 1,511.4 pages and 35.7 pages, respectively.The his torical average lifetime for cartridges produced by the current Pocess is 1,502.5 pages; the historical standard deviation is 97.3 pages.

a. What are the appropriate null and alternative hypotheses to test whether the mean lifetime of the new cartridges exceeds that of the old cartridges?

b. Use cu = .005 to conduct the test in part

a. Do the new cartridges have an average lifetime that is statistically significantly longer than thc cartridges currently in production?

c. Does the difference in average lifetimes appear to be of practical significance from the perspective of the consumer'? Explain.

d. Should the apparent decrease in the standard deviation in lifetimes associated with the new cartridges be viewed as an improvement over the old cartridges? Explain.