Question

Benson Manufacturing is considering ordering electronic
components from three different suppliers. The suppliers may differ
in terms of quality in that the proportion or percentage of
defective components may differ among the suppliers. To evaluate
the proportion defective components for the suppliers, Benson has
requested a sample shipment of 500 components from each supplier.
The number of defective components and the number of good
components found in each shipment is as
follows.

Supplier |
|||

Component |
A |
B |
C |

Defective |
10 | 30 | 50 |

Good |
490 | 470 | 450 |

**a.** Formulate the hypotheses that can be used to
test for equal proportions of defective components provided by the
three suppliers.

1. |
H _{0}: p _{1} ≠ p
_{2} = p _{3} |

2. |
H _{0}: p _{1} = p
_{2} = p _{3} |

3. |
H _{0}: p _{1} ≠ p
_{2} ≠ p _{3} |

Choose correct answer from above choice

- Select your answer -123Item 1

*H* _{a}: - Select your answer -All
population proportions are equalNot all population proportions are
equalItem 2

**b.** Using a .05 level of significance, conduct
the hypothesis test. What is the *p*-value? Use
Table 12.4.

The *p*-value is - Select your
answer -less than or equal .05greater than .05Item 3

What is your conclusion?

- Select your answer -Conclude that the three suppliers provide
equal proportions of defective components.Conclude that the three
suppliers do not provide equal proportions of defective
components.Item 4

**c.** Conduct a multiple comparison test to
determine if there is an overall best supplier or if one supplier
can be eliminated because of poor quality.
Round *p* _{i}, *p*
_{j} and difference to two decimal places. Round critical
value to four decimal places.

Comparison |
p _{i} |
p _{j} |
Difference |
n _{i} |
n _{j} |
Critical Value |
Significant Diff > CV |

A vs B | - Select your answer -YesNoItem 11 | ||||||

A vs C | - Select your answer -YesNoItem 18 | ||||||

B vs C | - Select your answer -YesNoItem 25 |

Answer #1

a)

*H* _{0}: *p* _{1} = *p*
_{2} = *p* _{3}

Ha:Not all population proportions are equal

b)

p value is less than or equal .05

.Conclude that the three suppliers do not provide equal proportions of defective components

c)

p̅1= | 0.02 |

p̅2= | 0.06 |

p̅3= | 0.1 |

for 2 df and 0.05 level: X^{2} = |
5.9915 |

As Criitcal value
=√X^{2}*√(p̅1*(1-p̅1)/n1+p̅2*(1-p̅2)/n2) |

critical val | ||||||||

Comparison | pi | pj | |abs diff| | ni | nj | value | significant diff >CV | |

1 vs 2 | 0.02 | 0.06 | 0.04 | 500 | 500 | 0.0302 | significant difference | |

1 vs 3 | 0.02 | 0.10 | 0.08 | 500 | 500 | 0.0362 | significant difference | |

2 vs 3 | 0.06 | 0.10 | 0.04 | 500 | 500 | 0.0419 | not significant difference |

Benson Manufacturing is considering ordering electronic
components from three different suppliers. The suppliers may differ
in terms of quality in that the proportion or percentage of
defective components may differ among the suppliers. To evaluate
the proportion of defective components for the suppliers, Benson
has requested a sample shipment of 500 components from each
supplier. The number of defective components and the number of good
components found in each shipment are as follows. Component
Supplier A B C Defective 15...

Use the sample data below to test the hypotheses
H 0: p 1
= p 2 = p
3
H a: Not all population proportions are the
same
Populations
Response
1
2
3
Yes
150
150
92
No
100
150
108
where p i is the population
proportion of yes responses for population i.
Using a .05 level of significance. Use Table 12.4.
a. Compute the sample proportion for each
population. Round your answers to two decimal places.
p̄ 1 =
p̄ 2 =
p̄...

Edwards Manufacturing Company purchases two component parts from
three different suppliers. The suppliers have limited capacity, and
no one supplier can meet all the company’s needs. In addition, the
suppliers charge different prices for the components. Component
price data (in price per unit) are as follows:
Supplier
Component
1
2
3
1
$12
$14
$10
2
$14
$12
$10
Each supplier has a limited capacity in terms of the total
number of components it can supply. However, as long as...

Edwards Manufacturing Company purchases two component parts from
three different suppliers. The suppliers have limited capacity, and
no one supplier can meet all the company’s needs. In addition, the
suppliers charge different prices for the components. Component
price data (in price per unit) are as follows:
Supplier
Component
1
2
3
1
$12
$13
$10
2
$11
$12
$10
Each supplier has a limited capacity in terms of the total
number of components it can supply. However, as long as...

Edwards Manufacturing Company purchases two component parts from
three different suppliers. The suppliers have limited capacity, and
no one supplier can meet all the company’s needs. In addition, the
suppliers charge different prices for the components. Component
price data (in price per unit) are as follows:
Supplier
Component
1
2
3
1
$12
$13
$10
2
$15
$12
$10
Each supplier has a limited capacity in terms of the total
number of components it can supply. However, as long as...

Edwards Manufacturing Company purchases two component parts from
three different suppliers. The suppliers have limited capacity, and
no one supplier can meet all the company’s needs. In addition, the
suppliers charge different prices for the components. Component
price data (in price per unit) are as follows:
Supplier
Component
1
2
3
1
$12
$14
$10
2
$14
$12
$10
Each supplier has a limited capacity in terms of the total
number of components it can supply. However, as long as...

Problem 4-11 (Algorithmic)
Edwards Manufacturing Company purchases two component parts from
three different suppliers. The suppliers have limited capacity, and
no one supplier can meet all the company’s needs. In addition, the
suppliers charge different prices for the components. Component
price data (in price per unit) are as follows:
Supplier
Component
1
2
3
1
$11
$12
$15
2
$11
$14
$11
Each supplier has a limited capacity in terms of the total
number of components it can supply. However,...

Edwards Manufacturing Company purchases two component parts from
three different suppliers. The suppliers have limited capacity, and
no one supplier can meet all the company’s needs. In addition, the
suppliers charge different prices for the components. Component
price data (in price per unit) are as follows:
Supplier
Component
1
2
3
1
$10
$14
$13
2
$12
$12
$12
Each supplier has a limited capacity in terms of the total
number of components it can supply. However, as long as...

Problem 9-11 (Algorithmic)
Edwards Manufacturing Company purchases two component parts from
three different suppliers. The suppliers have limited capacity, and
no one supplier can meet all the company’s needs. In addition, the
suppliers charge different prices for the components. Component
price data (in price per unit) are as follows:
Supplier
Component
1
2
3
1
$11
$11
$13
2
$10
$12
$10
Each supplier has a limited capacity in terms of the total
number of components it can supply. However,...

A large manufacturer purchases an identical component from three
independent suppliers that differ in unit price and quantity
supplied. The relevant data for 2012 and 2014 are given here.
Unit Price ($)
Supplier
Quantity (2012)
2012
2014
A
150
5.45
6.00
B
200
5.60
5.95
C
160
5.50
6.70
(a)
Compute the price relatives (index number) for each of the
component suppliers separately using 2012 as the base year. (Round
your answers to the nearest integer.)
Item
Price Relative
A...

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