Question

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 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. Please write down the symbolic form of the hypotheses.

Answer 1

The test hypothesis is :

`H_0: \mu=1502.5\\ H_a: \mu>1502.5`

Explanation:

Consider the provided information.

Null hypothesis refer the population parameter is equal to the claimed value.

If there is no statistical significance in the test then it is know as the null which is denoted by
`H_0`, otherwise it is known as alternative hypothesis which denoted by
`H_a`.

The historical average lifetime for cartridges produced by the current process is 1502.5 pages.

Hence, the test hypothesis is :

`H_0: \mu=1502.5\\ H_a: \mu>1502.5`