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.

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...

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...

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...

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