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: 2 0 3 1 8% Emrors per Invokce Percentage of Invoices More Than 3 5% 4% 80 % 3% After implementation of the computerized system, a random sample of 500 invoicess gives the following error distribution: ETors per Invoice Number of Invoices More Than 3 1 2 6 3 5 467 18 4 Ei 400 (f-E) 2/E 11.2225 12.1000 pi 0.80 fi 467 0,08 40 18 0.05 25 6 11.4400 0.04 20 5 11.2500 0.03 15 4 8.0667 57.07920 p-value 0.0000001096 Chi-Square (a) Shaw that it is apprapriate to carry out a chi-square test using these data. Each E (b) Use the Excel output ahown above to determine whether the error percentages for the computerized system differ from thoae for the manual system at the.05 level of aignificance. What do you conclude? Ho: Conclude aystema differ Reject

Answer 1

(a) Each E_{​​​​​​i^​​​} ≥ 5

>> The chi-square approximation relies on the counts being approximately normally distributed; when all the expectations are greater than or equal to 5.

(b) Reject H_{​​​​​​0}: Conclude systems differ.

>> As the p-value for this test is less than the significance level of 0.05, we reject H_{​​​​​​0} and conclude that the systems differ.