A company is said to be out of compliance if more than 10 of

A company is said to be out of compliance if more than 10% of all invoices contain errors, and it is considered to be seriously out of compliance if more than 15% of all invoices contain errors. Suppose an auditor randomly selects a sample of 1250 invoices and found that 200 contained errors.

a) Construct a 95% confidence interval for this company\'s error rate.

b) What is the probability a company would be rated as seriously out of compliance by this test if 18% of all invoices at that company contain errors?

c) What sample size should the auditor use to estimate the error rate to within 2% with 99% confidence if it is assumed that the error rate will be no more than 20%?

Solution

Sample size n =1250; proportion of erros = 200/1250=

SE=0.010369; Z value at 5% LOS = 1.96

95% confidence interval = (0.16-1.96*SE, 0.16+1.96*SE)=(0.139677,

b) NH : P=0.15 AH: P>0.15

Here SE = Sqrt((0.15*0.85)/1250)=0.0101

Z= (0.18-0.15)/0.0101 =2.9704

P-value of this test = P(Z>2.9704) = 0.0015

the probability a company would be rated as seriously out of compliance by this test if 18% of all invoices at that company contain errors = 0.0015

C)

Sample Size for Estimation

Method

Parameter Proportion
Distribution Binomial
Proportion 0.2
Confidence level 99%
Confidence interval Upper bound

Results

Margin Sample
of Error Size
0.02 2330

Sample size =2330