Question

An auditor wants to know the (population) proportion (p) of companies under audit that may have financial distress. Before she starts to collect data, she needs to determine the sample size (n) in the random sample that she is going to take. If the auditor wants to be 95% confident that the maximum difference between the unbiased point estimator and pto be 0.02, determine nif

1. she has no prior knowledge about p;

her prior knowledge about pfrom the previous three years is p= 0.15.   

Answer 1

Margin of error = Z*

i. Without any prior estimate of p, assume p as 0.5

Given margin of error = 0.02

For 95% confidence level, Z* = 1.96

0.02 = 1.96 x

= 49

n = 2401

ii. When p = 0.15

0.02 = 1.96 x

= 34.99

n = 1225