A CPA’s client is considering adoption of statistical sampling techniques. Accordingly, he has asked the CPA to discuss these techniques at a meeting of client employees. In connection with this presentation, the CPA prepared the following table, which shows the comparative characteristics of two populations and the samples to be drawn from each. For example, in Case 1, the variability of population 1 is smaller than that of population 2, whereas the populations are of equal size and the samples to be drawn from them have equal specified precisions (confidence intervals) and specified reliabilities (confidence levels).

Using the table and the technique of unrestricted random sampling with replacement, meeting participants are to be asked to determine the relative required sample sizes to be drawn from the two populations. Each of the five cases is independent of the other four and is to be considered separately. Choose the best response for each.

a. The required sample size from population 1 in case 1 is:
(i) Larger than the required sample size from population 2 (ii) Equal to the required sample size from population 2 (iii) Smaller than the required sample size from population 2 (iv) Indeterminate relative to the required sample size from population 2

b. The required sample size from population 1 in case 2 is:
(i) Larger than the required sample size from population 2 (ii) Equal to the required sample size from population 2 (iii) Smaller than the required sample size from population 2 (iv) Indeterminate relative to the required sample size from population 2

c. The required sample size from population 1 in case 3 is:
(i) Larger than the required sample size from population 2 (ii) Equal to the required sample size from population 2 (iii) Smaller than the required sample size from population 2 (iv) Indeterminate relative to the required sample size from population 2

d. The required sample size from population 1 in case 4 is:
(i) Larger than the required sample size from population 2 (ii) Equal to the required sample size from population 2 (iii) Smaller than the required sample size from population 2 (iv) Indeterminate relative to the required sample size from population 2

e. The required sample size from population 1 in case 5 is:
(i) Larger than the required sample size from population 2 (ii) Equal to the required sample size from population 2 (iii) Smaller than the required sample size from population 2 (iv) Indeterminate relative to the required sample size from population 2

Population I relative to population 2 Sample from population 1 relative to sample from population 2 Specified Specified Size Variability precision reliability Case 1 Equal Smaller Equal Equal Case 2 Smaller Equal Equal Higher Case 3 Equal Equal Wider Equal Case 4 Larger Equal Narrower Equal Case 5. Equal Greater Equal Higher