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	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 E_i ≥                 

(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.

Answer 1

(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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