Problem 90E

Invoice errors in a billing system. In a study of invoice errors in a company’s new billing system, an auditor randomly sampled 35 invoices produced by the new system and recorded actual amount (A), invoice amount (I), and the difference (or error), x = (A - I). The results were = $1 and s = +124. At the time that the sample was drawn, the new system had produced 1,500 invoices. Use this information to find an approximate 95% confidence interval for the true mean error per invoice of the new system. Interpret the result.

Solution :

Step 1 of 1:

The given problem explain about invoice errors in a billing system.

Let N denotes the population size is 1500 invoices.

Let n denotes the sample size is 35 invoices.

Let denotes the sample mean of invoices is $1 and

Let s denotes the standard deviation of the invoices is $124.

Our goal is:

We need to find an approximate 95% confidence interval for the true mean error per invoice of the new system.

Now we have to find an approximate 95% confidence interval for the true mean error per invoice of the new system.

Now we have to find the approximate 95% confidence interval.

Then the estimated standard error is

We know that n, N, and s.

20.7137

Therefore, the estimated standard error is 20.7137.

Then the approximate 95% confidence interval is

We know that= 1 and = 20.7137.

=

=

= (1-41.43, 1+41.43)

= (-40.43, 42.43)

Hence a 95% confidence interval for the true mean error per invoice of the new system is between -$40.43 and $42.43.