Question

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 $11,153.8. Set up the hypotheses.

Conduct the hypothesis testing at a level of significance of 5%. Use both critical value approach and p-value approach.

Answer 1

Solution :

= 100,000

=92,172

s =11,153.8

n = 75

This is the two tailed test .

The null and alternative hypothesis is ,

H₀ :    = 100,000

H_a :     100,000

Test statistic = t

= ( - ) / s / n

= (92,172-100,000) / 11,153.8 / 75

= −6.298

Test statistic = t =  −6.298

P-value = 0

= 0.05  

P-value <

0 < 0.05

Reject the null hypothesis .

There is sufficient evidence to suggest that   

It is observed that I∣t∣=6.298>tc​=1.993, it is then concluded that the null hypothesis is rejected