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. 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.

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.

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.

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