A company has developed a new ink-jet cartridge for its printer that it believes has a longer lifetime on average than the one currently being produced. To investigate its length of life, 240 of the new cartridges were tested by counting the number of high-quality printed pages each was able to produce. The sample mean and standard deviation were determined to be 1511.4 pages and 35.7 pages, respectively. The historical average lifetime for cartridges produced by the current process is 1502.5 pages. At α = .05, test the claim that the new cartridge has a longer lifetime.