A wholesaler has recently developed a computerized salesinvoicing system. Prio t

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A wholesaler has recently developed a computerized salesinvoicing system. Prio to implementing this system, a manualsystem was used. The distribution of the number of errors perinvoice for the manual system is as follows: Errors perInvoice                        0         1         2         3      MoreThan 3 Percentage ofInvoices               87%   8%     3%     1%     1% After implementaion of the computerized system, a randomsample of 500 invoices gives the following errordistributions: Errors perInvoice                        0         1         2         3      MoreThan 3 Number ofInvoices                 479      10        8         2       1 a. Show that it s appropriate to carry out a chi-squaretest using these data. b. Use the following Excel output to determine whether theerror percentages for the computerized system differ from those forthe manual system at the .05 level of significance. What doyou conclude? pi                                 Ei                        fi                               (f=-E)^2/E 0.87                           435                     479                              4.4506 0.08                           40                        10                                22.5000 0.03                           15                        8                                   3.2667 0.01                           5                           1                                 1.8000 0.01                           5                           1                                 3.2000                                       Chi-                             35.21724  p-value 0.0000001096 square A wholesaler has recently developed a computerized salesinvoicing system. Prio to implementing this system, a manualsystem was used. The distribution of the number of errors perinvoice for the manual system is as follows: Errors perInvoice                        0         1         2         3      MoreThan 3 Percentage ofInvoices               87%   8%     3%     1%     1% After implementaion of the computerized system, a randomsample of 500 invoices gives the following errordistributions: Errors perInvoice                        0         1         2         3      MoreThan 3 Number ofInvoices                 479      10        8         2       1 a. Show that it s appropriate to carry out a chi-squaretest using these data. b. Use the following Excel output to determine whether theerror percentages for the computerized system differ from those forthe manual system at the .05 level of significance. What doyou conclude? pi                                 Ei                        fi                               (f=-E)^2/E 0.87                           435                     479                              4.4506 0.08                           40                        10                                22.5000 0.03                           15                        8                                   3.2667 0.01                           5                           1                                 1.8000 0.01                           5                           1                                 3.2000                                       Chi-                             35.21724  p-value 0.0000001096 square Errors perInvoice                        0         1         2         3      MoreThan 3 Number ofInvoices                 479      10        8         2       1 a. Show that it s appropriate to carry out a chi-squaretest using these data. b. Use the following Excel output to determine whether theerror percentages for the computerized system differ from those forthe manual system at the .05 level of significance. What doyou conclude? pi                                 Ei                        fi                               (f=-E)^2/E 0.87                           435                     479                              4.4506 0.08                           40                        10                                22.5000 0.03                           15                        8                                   3.2667 0.01                           5                           1                                 1.8000 0.01                           5                           1                                 3.2000                                       Chi-                             35.21724  p-value 0.0000001096 square

Explanation / Answer

a. H0 : The error percentages for the computerizedsystem are same as from those for the manualsystem     Ha : The error percentages forthe computerized system differ from those for the manualsystem Since we want to check the goodness of fit of results fromcomputerized system, the Chi - square test for goodness of fit isappropriate test procedure here. b. The p-value 0.0000001096 is very small ans < 0.05, sothe data provides strong evidence at 5% level, to support the claimthat the error percentages for the computerized system differ fromthose for the manual system.

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