Question

A wholesaler has recently developed a computerized sales invoicing system. Prior to implementing this system, a manual system was used. Historically, the manual system produced 87% of invoices with 0 errors, 8% of invoices with 1 error, 3% of invoices with 2 errors, 1% of invoices with 3 errors, and 1% of invoices with more than 3 errors.

After implementation of the computerized system, a random sample of 500 invoices showed 479 invoices with 0 errors, 10 invoices with 1 error, 8 invoices with 2 errors, 2 invoices with 3 errors, and 1 invoice with more than 3 errors.

Tasks:

Create appropriate null and alternative hypotheses.

Justify the appropriate chi-square test to determine whether the error percentages for the computerized system differ from the normal system.

The chi-square statistic and p-values are 35.22 and < 0.0001. Interpret the p value for an accept/reject decision regarding the hypothesis. Choose the standard level of significance.

State your conclusion.

Answer 1

H0: If the data is consistent with specified distribution

Ha: If the data is not consistent

df= (r-1) = 4

let assume:

Critical value:

Test statistic:

Expected value(E) = Proportion* Sample

Invoice	Probability	Sample	Expected	(O-E)^2	(O-E)^2/E
0	0.87	479	435	1936	4.450575
1	0.08	10	40	900	22.5
2	0.03	8	15	49	3.266667
3	0.01	2	5	9	1.8
3+	0.01	1	5	16	3.2
				Sum	35.21724

The test statistic is significant at significant level 0.05 and Rejects H0. There is enough evidence to support the claim that the data is different from population proportion.