In the following situations solve the problems and answer the questions.

a. Non statistical sampling is used. The number of items in the population is 1,000 , and the recorded amount on the books is \(\$ 100,000\). The sample size is 250 , and the recorded amount of the sample is \(\$ 40,000\). The audit amount of the sample is \(\$ 35,000\) based on five misstatements.

(1) Calculate the projected misstatement using two methods. Show the calculations for both methods.

(2) Explain why there was a difference in the projected misstatements. Under what conditions should each projected misstatement be used?

b. PPS sampling is used. The sampling interval is \(\$ 6,000\). One misstatement is found. The recorded amount of the account in which the misstatement was found is \(\$ 5,000\), and the audited amount is \(\$ 3,500\).

(1) Calculate the projected misstatement. Show calculations.

(2) Explain the commonality between the method of calculating the projected misstatement here and one of the methods of calculating the projected misstatement in

(a) above.