Question

1. A bank president claims that the median of debt-to-equity ratio of commercial loans provided is less than 1.5. A random sample of 15 commercial loans is selected with the following values for this ratio:

1.31                 1.33                 1.22

1.78                 1.45                 1.32

1.46                 1.41                 1.19

1.05                 1.29                 1.11

1.37                 1.21                 1.65

           

Use a Sign Test at the 0.05 level to test this claim. Do this by hand and not using Excel. (15 points)

Answer 1

Out of 15 values 2 are above 1.5 and 13 are below 1.5

.The provided number of positive signs is and the number of negative signs is .

(1) Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

Ho: Median of Differences ≥ 1.5

Ha: Median of Differences < 1.5

The test statistic is

(2) Rejection Region

The critical value for the signficance level provided and the type of tail is

(3) Decision about the null hypothesis

Since in this case , there is enough evidence to claim that the population median of differences is less than 1.5, at the 0.05 significance level.