Problem:
A wholesaler has recently developed a computerized sales invoicing system. Prior to implementing this system, a manual system was used. The distribution of the number of errors per invoice for the manual system is as follows:
Errors per invoice 0 1 2 3 3 or more
Percentage of Invoices 87% 8% 3% 1% 1%
After implementation of the computerized system, a random sample of 500 invoices gives the following error distribution:
Errors per invoice 0 1 2 3 more than 3
Number of Invoices 479 10 8 2 1
Q1. Show that it is appropriate to carry out a chi-square test using these data.
Q2. Use the following Excel output to determine whether the error percentages for the computerized system differ from those for the manual system at the .05 level of significance. What do you conclude?
pi Ei fi (f-E) ^2/E
0.87 435 479 4.4506
0.08 40 10 22.5000
0.03 15 8 3.2667
0.01 5 2 1.8000
0.01 5 1 3.2000
Chi-Square 35.21724
p-value 0.00000001096.