Question

The Office of the Superintendent of Bankruptcy of Canada (OSBC) is developing a new index to measure the vulnerability of firms in the new technology industry. The index is a ratio of current assets to current liabilities adjusted for various factors specific to this industry. The OSBC wants to compare the index among healthy and failed firms for validation purposes. They expect that failed firms should have a lower index than the healthy ones. Based on a Canadian business registry, they draw a random sample of 68 firms still in operations and another random sample of 33 firms which failed in the last 3 years.

Healthy   Failed
1.50   0.82
2.08   0.05
2.23   1.68
0.89   0.91
1.91   1.16
1.20   0.42
1.95   0.88
2.73   1.11
1.62   2.03
1.71   0.92
1.03   0.73
1.96   0.89
0.10   0.83
1.43   0.99
2.50   0.52
0.23   1.32
1.67   0.48
2.17   1.10
2.61   0.19
1.56   0.51
1.76   0.26
1.02   0.88
1.80   1.31
1.81   0.90
1.76   0.62
0.68   1.45
2.02   1.17
1.20   0.93
1.87   0.75
2.61   0.13
1.11   1.12
2.73   1.15
2.22   0.71
2.50  
0.67  
1.14  
3.15  
1.44  
2.16  
1.21  
3.05  
0.95  
0.90  
2.80  
1.55  
2.44  
1.84  
1.24  
1.39  
1.80  
2.05  
1.52  
0.96  
2.12  
1.85  
1.69  
2.30  
2.21  
2.03  
1.64  
1.87  
1.06  
1.93  
2.25  
1.42  
0.96  
1.64  
2.21  

a) Use Minitab or other appropriate software to produce boxplots of the index values for the two groups of firms and comment on their distribution. 2

b) Use an appropriate statistical test to determine, at the 1% significance level, whether the data provide evidence of a higher average index for the healthy firms. Make sure you provide your manual calculations using the critical value approach.

c) Calculate manually a 99% one-sided confidence interval for the difference in the average index of healthy and failed firms and compare your results with b) above.

d) Use Minitab or other appropriate software to perform the calculations in b) and c) above and comment on any differences.

Answer 1