Problem II. One measure of a company’s financial health is its debt-to-equity ra

Question

Problem II. One measure of a company’s financial health is its debt-to-equity ratio. This quantity is defined to be the ratio of the company’s corporate debt to the company’s equity. If this ratio is to high, it is one indication of financial instability. Banks often monitor the financial health of companies to which they have extended commercial loans. A “lean” debt-to-equity ratio is considered to be a ratio of 1.50. A particular bank ran an audit for its loan portfolio’s debt-to-equity ratio and randomly selected a sample of 15 of its commercial loan accounts, producing the follow result:

1.32 1.27 1.45 1.67 1.73

1.49 1.59 1.09 1.26 1.78

1.36 1.65 1.54 1.69 1.38

The sample mean and standard deviation for above sample are, x =1.485,s=0.202

Find a 98% confidence interval for the bank’s debt-to-equity ratio for its loan portfolio.

Lower bound:

Upper bound:

Interpret the results you found in item 3.

Explanation / Answer

From the given data, we calculate

CI = (1.2896, 1.6804)

As the value of lean debt to equity ratio of 1.5 lies within the confidence interval, Bank has sufficient evidence to conclude that ratio is lean.

CI for 98% mean 1.485 std.dev. 0.202 n 15 t-value 3.7469 SE = std.dev./sqrt(n) 0.0522 ME = t*SE 0.1954 lower limit = mean - ME 1.2896 upper limit = mean + ME 1.6804

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