A firm's president, vice presidents, department managers, and others use financial data generated by the firm's accounting system to help them make decisions regarding such things as pricing, budgeting, and plant expansion. To provide reasonable certainty that the system provides reliable data, internal auditors periodically perform various checks of the system (Horngren, Foster, and Datar, Cost Accounting: A Managerial Emphasis, 2005). Suppose an internal auditor is interested in determining the proportion of sales invoices in a population of 5,000 sales invoices for which the "total sales" figure is in error. She plans to estimate the true proportion of invoices in error based on a random sample of size 100.
a. Assume that the population of invoices is numbered from 1 to 5,000 and that every invoice ending with a 0 is in error (i.e., 10% are in error). Use a random number generator to draw a random sample of 100 invoices from the population of 5,000 invoices. For example, random number 456 stands for invoice number 456. List the invoice numbers in your sample and indicate which of your sampled invoices are in error (i.e., those ending in a 0).
b. Use the results of your sample of part a to construct a 90% confidence interval for the true proportion of invoices in error.
c. Recall that the true population proportion of invoices in error is equal to .1. Compare the true proportion with the estimate of the true proportion you developed in part b. Does your confidence interval include the true proportion?