Data Utilities

   Financial   analysts specializing in credit markets are often interested in creating   models to predict whether a firm will go bankrupt within some fixed period of   time. If there is a good chance that a particular firm will go bankrupt,   then, the firm will have to pay a very high interest rate on any debt (bonds)   that it may issue. In practice, statistical models to predict bankruptcy are   fairly difficult to construct. One of the variables that may be useful in   distinguishing between firms that go bankrupt and firms that stay solvent is   the return on assets (ROA). The accompanying file Bankruptcy.xls contains financial data on 44 firms. Of these 44 firms, 20 firms went bankrupt within   1 year after the data were collected; the other 24 firms remained solvent   after 1 year.

For this assignment, ignore all financial measures other than   ROA. As a first step, unstack the ROA variable (see Data Utilities menu in   StatTools) using “Bankrupt” as the code variable (in the menu set Bankrupt as   the “cat” variable and ROA as the “Val”). Now you should have two columns of   ROA data in a new worksheet. For the purpose of this exercise we will assume   that firms’ ROA is in general normally distributed. a) Construct a 90%   confidence interval for the average ROA of firms that remained solvent.

i. Attach the StatTools output as Exhibit A or use the space below to show how   you calculated the confidence interval. ii. In the space below, state the confidence interval below in the form: point estimate margin of error.   

b) Test the hypothesis that the average ROA of firms that went bankrupt is less than -5%.

i. Attach the StatTools output as Exhibit B or use the space below to demonstrate the main   steps in your calculations. ii. State the p-value for this hypothesis test.   

iii. At the 10% level of significance, is the average ROA of   firms that went bankrupt less than -5%? (Circle one.) Yes No    

      ASST_SLS BANKRUPT   0.13 No   0.18 No   0.20 No   0.26 No   0.30 No   0.33 No   0.35 No   0.35 No   0.38 No   0.40 No   0.44 No   0.45 No   0.47 No   0.48 No   0.52 No   0.52 No   0.53 No   0.54 No   0.55 No   0.56 No   0.58 No   0.63 No   0.69 No   0.69 No   0.17 Yes   0.18 Yes   0.25 Yes   0.26 Yes   0.27 Yes   0.28 Yes   0.34 Yes   0.38 Yes   0.40 Yes   0.40 Yes   0.42 Yes   0.43 Yes   0.45 Yes   0.51 Yes   0.60 Yes   0.66 Yes   0.67 Yes   0.70 Yes   0.71 Yes   0.95 Yes