Question

The IMF is an international organization of 189-member countries that, among other things, looks to assist nations that can’t pay their international debt obligations.

Assume that a financial analyst for the IMF was reading the study “Analysis and Modeling of Recent Business Failures in Greece,” in Managerial and Decisions Economics (1992). In this study, the authors compared various characteristics of firms that failed against firms that succeeded. One of the variables studied was the Current Ratio of firms. This is a measure of liquidity that measures the ratio of Current Assets to Current Liabilities. Generally speaking, the Current Ratio of a company is roughly the amount a firm is worth divided by what it owes. For a sample of 68 firms that succeeded, the average Current Ratio was 1.73 with a standard deviation of .64. For a sample of 33 firms that failed, the average Current Ratio was .82 with a standard deviation of .48. At the 5% level of significance, test the hypothesis that the Current Ratio of successful firms is significantly greater than that of unsuccessful firms.

A. since the t-score of 7.2 is greater than the critical t-score of 1.66, we reject the null hypothesis that the current ratio of successful firms is less than or equal to that of unsuccessful firms. There is some evidence to suggest that the current ratio of successful firms might be greater than that of unsuccessful firms.

B. since the t-score of 7.2 is greater than the critical t-score of 1.66, we cannot reject the null hypothesis that the current ratio of successful firms is less than or equal to that of unsuccessful firms. There is some evidence to suggest that the current ratio of successful firms might be greater than that of unsuccessful firms.

C. since the t-score of 7.2 is greater than the critical t-score of 1.66, we reject the null hypothesis that the current ratio of successful firms greater than or equal to that of unsuccessful firms. There is some evidence to suggest that the current ratio of successful firms might be less than that of unsuccessful firms.

D. since the t-score of 7.2 is greater than the critical t-score of 1.66, we cannot reject the null hypothesis that the current ratio of successful firms is greater or equal to that of unsuccessful firms. There is some evidence to suggest that the current ratio of successful firms might be greater than that of unsuccessful firms. <br>e, none of these answers are correct

Answer 1

Succeeded: = 1.73, s1 = 0.64, n1 = 68

Failed: = 0.82, s2 = 0.48, n2 = 33

The Hypothesis:

H0:

Ha: >

Since s1/s2 = 1.33 (< 2) we use the pooled variance

The degrees of freedom used is n1 + n2 - 2 = 68 + 33 - 2 = 99 (since pooled variance is used)

The Test Statistic:

The Critical Value: For = 0.05, df = 99, critical value = 1.66

The Rejection Rule: Reject H0, if t observed is > t critical.

Therefore Option A: Since the t - score of 7.2 is greater than the critical t - score of 1.66, we reject the null hypothesis that the current ratio of successful firms is less than or equal to that of the unsuccessful firms.

There is some evidence to suggest that the current ratio of successful firms is greater than that of unsuccessful firms.