A wholesaler has recently developed a computerized sales invoicing system. Prior

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

Errors per invoice 0 1 2 3 More than 3
Percentage of invoices 87% 8% 3% 1% 1%

After implementation of the computerized system, a random sample of 500 invoice gives the following error distribution:

Error per invoice 0 1 2 3 More than 3
Number of invoices 479 10 8 2 1

a. Show that it is appropriate to carry out a chi-square test using these data.
b. Use the following Excel output to determine whether the error percentages for the computerized system differ from those for the manual system at the 0.5 level of significance. What do you conclude?

Explanation / Answer

Error/invoice manual Expected Ei Observed Fi (Ei-Fi)²/Ei


0 87% 435 479 4.450575


1 8% 40 10 22.5


2 3% 15 8 3.266667


3 1% 5 2 1.8


> 3 1% 5 1 3.2













Total = chi-square = 35.21724





critical value = 9.487729





p-value = 4.19E-07










Chi-square is appropriate because they are independednt radom observation,

and sample size is sufficient (500) and each expected frequency is sufficiently large (=5)








Since p-value is very very small, we reject hypothesis of no difference. We conclude the two systems differ. Error/invoice manual Expected Ei Observed Fi (Ei-Fi)²/Ei


0 87% 435 479 4.450575


1 8% 40 10 22.5


2 3% 15 8 3.266667


3 1% 5 2 1.8


> 3 1% 5 1 3.2













Total = chi-square = 35.21724





critical value = 9.487729





p-value = 4.19E-07










Chi-square is appropriate because they are independednt radom observation,

and sample size is sufficient (500) and each expected frequency is sufficiently large (=5)








Since p-value is very very small, we reject hypothesis of no difference. We conclude the two systems differ.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.