A wholesaler has recently developed a computerized sales invoicing system. Prior
ID: 3229486 • Letter: A
Question
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:
After implementation of the computerized system, a random sample of 500 invoices gives the following error distribution:
Use the Excel output shown above 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?
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 More Than 3 Percentage of Invoices 80% 8% 5% 4% 3%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 467 18 6 5 4 pi Ei fi (f – E) ^ 2/E 0.80 400 467 11.2225 0.08 40 18 12.1000 0.05 25 6 14.4400 0.04 20 5 11.2500 0.03 15 4 8.0667 Chi-Square 57.07920 p-value 0.0000001096 (a) Show that it is appropriate to carry out a chi-square test using these data. Each Ei (b)Use the Excel output shown above 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?
Explanation / Answer
a, each Ei is greater than or equal to 15
b, here pvalue<0.05 therefore, the error percentages for the computerized system differ from those for the manual system at the .05 level of significance.
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