When implementing a packaged Enterprise Resource Planning $($ERP$)$ system, many

firms report that the most important module $($usually the first one to be installed$)$ is Financial

Accounting. The hope is that this software will accelerate the financial close process of the firm.

Below is a sample of eight firms that reported their average time $($in weeks$)$ to financial close

before and after implementation of their ERP system.

Firm $12345678$

Before $6\mathrm{.}57\mathrm{.}08\mathrm{.}04\mathrm{.}55\mathrm{.}24\mathrm{.}95\mathrm{.}26\mathrm{.}5$

After $4\mathrm{.}25\mathrm{.}98\mathrm{.}04\mathrm{.}03\mathrm{.}84\mathrm{.}16\mathrm{.}04\mathrm{.}2$

a$)$ Formulate appropriate hypotheses to test the effectiveness of the ERP system. Discuss the

meaning of Type I and Type II error in this context, and select a confidence level $($either $95\%$

or $99\%)$ based on this discussion.

b$)$ Should you use a two$-$sample test, or a paired test? Justify your choice, then perform that test

and state your conclusion.