A company has developed a new ink-jet cartridge for its printer that it believes has a longer life-time 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 high-quality printed pages each was able to produce. The sample mean was determined to be 1511.4 pages. The population standard deviation is known to be 35.7 pages. The historical average lifetime for cartridges produced by the current process is 1502.5 pages.
-The null and alternative hypotheses to test whether the mean lifetime of the new cartridges exceeds that of the old cartridges is _____.

Question

Quizplus · Accepted Answer

The correct hypothesis to test whether the mean lifetime of the new cartridges exceeds that of the old cartridges is: Null hypothesis (H0): μ ≤ 1502.5 (the mean lifetime of the new cartridges is less than or equal to the historical average) versus Alternative hypothesis (H1): μ > 1502.5 (the mean lifetime of the new cartridges is greater than the historical average). This setup allows for testing if the new cartridges indeed have a longer life on average than the current ones.

A Company Has Developed a New Ink-Jet Cartridge for Its