A company has developed a new ink-jet cartridge for its printer that

1.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, 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 life-time.

2. Two different firms design their own tests for business graduates, and an employer administers both versions to a random selection of prospective employees. Results are below. At alpha=.02, test the claim that both versions produce the same score.
Mean difference = -4.25
standard error of the difference = 1.411
t-test: Paired Two Sample for Means
                                       Variable 1        Variable 2
Mean                             99.75                 104
Variance                        65.92857          48.28571
Observations                  8                       8
Pearson Correlation     .870992
Hypothesized Mean
Difference                       0
df                                       7
t Stat                                 -3.01193
P(T<=t) one-tail               .009804
tCritical one-tail              2.516752
P(T<=t) two-tail                 .019608
tCritical two-tail               2.997952