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.Calculate the appropriate test statistic to test the hypotheses.
A)56.09
B)3.74
C)22.34
D)-3.74
E)-22.34

Question

Quizplus · Accepted Answer

We use the one-sample t-test formula, where 
t = (sample mean - hypothesized mean)/(standard error of the mean)
The standard error of the mean is given by standard deviation/square root of sample size.
Plugging in the values, we get t = (1511.4 - 1502.5)/(35.7/sqrt(225)) = 3.74.
Therefore, the appropriate test statistic is 3.74, which corresponds to choice B.

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