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 |
80% | 8% | 5% | 4% | 3% |

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 |
462 | 15 | 10 | 8 | 5 |

pi | Ei | fi | (f – E) ^ 2/E | ||

0.80 | 400 | 462 | 9.6100 | ||

0.08 | 40 | 15 | 15.6250 | ||

0.05 | 25 | 10 | 9.0000 | ||

0.04 | 20 | 8 | 7.2000 | ||

0.03 | 15 | 5 | 6.6667 | ||

Chi-Square | 48.10170 | 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? |

Answer #1

Solution

Part (a)

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

**Each E_{i} ≥ 5**

Part (b)

p-value is extremely low, smaller than any conceivable significance level. This implies that the Chi-square statistic is highly significant. This, in turn means that the error rate for the computerized system differ from those for the manual system at the .05 level of significance.

Going further, a closer look at the error rates reveals that for all the rates of 1, 2, 3 and more than 3, fi < Ei indicating that in each of these rates computerized system performs much better.

For the rate 0, fi > Ei, further confirming that computerized system is far superior.

In quantitative terms, average error rate for computerized
system is just 0.15 per invoice whereas that for the manual system
is 0.42 per invoice, almost three-fold. **Answer
2**

**DONE**

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
84%
8%
3%
3%
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...

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
84%
7%
4%
3%
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...

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...

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