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 | 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 3 |

Number of Invoices | 465 | 16 | 10 | 6 | 3 |

pi | Ei | fi | (f – E) ^ 2/E | ||

0.82 | 410 | 465 | 7.3780 | ||

0.08 | 40 | 16 | 14.4000 | ||

0.04 | 20 | 10 | 5.0000 | ||

0.04 | 20 | 6 | 9.8000 | ||

0.02 | 10 | 3 | 4.9000 | ||

Chi-Square | 41.47800 | 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?

(Click to select)Do not rejectReject *H*_{0}:
Conclude systems (Click to select)not differdiffer.

Answer #1

(a)

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

Each E_{i}
5 as follows:

Expected values:

(b)

Since p - value = 0.00000001096 is less than = 0.05, the difference is significant. Reject null hypothesis.

Conclusion:

The data support the claim that the error percentages for the
computerized system differ from those for the manual system at the
0.05 level of significance.

So,

Correct option:

**Reject H0.**

**Conclude systems differ.**

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
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
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. 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...

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