Business bankruptcies in Canada are monitored by the Office of the Superintendent of

Bankruptcy Canada $($OSB$).$ Included in each report are the assets and liabilities the

company declared at the time of the bankruptcy filing. OSB is interested in finding out if

the mean debt $($liabilities minus assets$)$ across all bankruptcy cases is different from

$$100,000.$ A study is based on a random sample of $75$ reports from the current year.

The average debt is $$92,172.$ With a standard deviation of $$11,153\mathrm{.}8.$ Set up the

hypotheses. Conduct the hypothesis testing at a level of significance of $5\%.$ Use both

critical value approach and p$-$value approach.