The Office of the Superintendent of Bankruptcy of Canada (OSBC)is developing a new index to measure the vulnerability of firms inthe new technology industry. The index is a ratio of current assetsto current liabilities adjusted for various factors specific tothis industry. The OSBC wants to compare the index among healthyand failed firms for validation purposes. They expect that failedfirms should have a lower index than the healthy ones. Based on aCanadian business registry, they draw a random sample of 68 firmsstill in operations and another random sample of 33 firms whichfailed 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 boxplotsof the index values for the two groups of firms and comment ontheir distribution. 2

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

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

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