Question

Please answer question A, B, and C with the solution

Suppose we take a random sample of 30 companies in an industry of 200 companies. We calculate the sample mean of the ratio of cash flow to total debt for the prior year. We find that this ratio is 23 percent. Subsequently, we learn that the population cash flow to total debt ratio (taking into account of all 200 companies) is 26 percent. What is the explanation for the discrepancy between the sample mean of 23 percent and the population mean of 26 percent?

A. Sampling Error

B. Bias

C. A lack of Consistency Answer:

Answer 1

Bias is the case where the same estimator gives different results different times.

Lack of consistency refers to the lack of procedures followed in estimating a sample.

Sampling error means when that sample is taken into consideration which does not represent the entire population of the data and thus the result from estimating the sample and the population becomes different.

Here, a random sample of 30 companies in an industry of 200 companies gave been taken into consideration. The sample mean of the ratio of cash flow to total debt for the prior year is 23 percent. However, the population mean of the ratio is 26 percent. This discrepancy has occurred due to sample error. The difference in the values of the sample mean and the population mean has occurred because samples have been chosen of which every sample does not follow the properties of the population. Therefore, the population mean is 26 percent and that of the sample mean is 23 percent.

Therefore, option A stands correct here. The discrepancy vetebet the sample mean and the population mean has occurred due to Sampling Error.