Question

# A wholesaler has recently developed a computerized sales invoicing system. Prior to implementing this system, a...

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 84% 7% 4% 3% 2%

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 480 7 8 2 3
 pi Ei fi (f – E) ^ 2/E 0.84 420 480 8.5714 0.07 35 7 22.4000 0.04 20 8 7.2000 0.03 15 2 11.2667 0.02 10 3 4.9000 Chi-Square 54.33810 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?

(Click to select)RejectDo not reject H0: Conclude systems (Click to select)not differdiffer.

(a) Show that it is appropriate to carry out a chi-square test using these data.

Each Ei ≥ 5

(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?

Reject H0: Conclude systems differ.

 observed expected O - E (O - E)² / E 480 420.000 60.000 8.571 7 35.000 -28.000 22.400 8 20.000 -12.000 7.200 2 15.000 -13.000 11.267 3 10.000 -7.000 4.900 500 500.000 0.000 54.338 54.34 chi-square 4 df 4.47E-11 p-value

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