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	82%	8%	4%	4%	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	465	16	10	6	3

pi	Ei	fi	(f – E) ^ 2/E
0.82	410	465	7.3780
0.08	40	16	14.4000
0.04	20	10	5.0000
0.04	20	6	9.8000
0.02	10	3	4.9000
	Chi-Square		41.47800		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)Do not rejectReject H₀: Conclude systems (Click to select)not differdiffer.

Answer 1

(a)

It is appropriate to carry out a chi - square test using these data because

Each E_i 5 as follows:

Expected values:

(b)

Since p - value = 0.00000001096 is less than = 0.05, the difference is significant. Reject null hypothesis.

Conclusion:
The data support the claim that the error percentages for the computerized system differ from those for the manual system at the 0.05 level of significance.

So,

Correct option:

Reject H0.

Conclude systems differ.