Question

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 _{3} =

**b.** Use the multiple comparison procedure to
determine which population proportions differ significantly. Use a
.05 level of significance. 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 |

1 vs 2 | - Select your answer -YesNoItem 10 | ||||||

1 vs 3 | - Select your answer -YesNoItem 17 | ||||||

2 vs 3 | - Select your answer -YesNoItem 24 |

- Select your answer -1 and 21 and 32 and 3none of themItem 25

Answer #1

a)

p̅1=150/250= | 0.6 |

p̅2=150/300= | 0.5 |

p̅3=92/200 = | 0.46 |

b)

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 | 0.60 | 0.50 | 0.10 | 250 | 300 | 0.1037 | not significant difference |

1 vs 3 | 0.60 | 0.46 | 0.14 | 250 | 200 | 0.1149 | significant difference |

2 vs 3 | 0.50 | 0.46 | 0.04 | 300 | 200 | 0.1115 | not significant difference |

1 vs 3 are different

Use the sample data to test the hypothesis. H0:p1=p2=p3. Ha:Not
all population proportions are the same
Population 1: yes 150 no 100. Population 2: yes 150 no 150.
Population 3: yes 91 no 109.
where Pi is the population proportion of yes responses for
population i. Using a .05 level of significance.
Compute the sample proportion for each population. Round your
answers to two decimal places. P1=? P2=?P3?
Use the multiple comparison procedure to determine which
population proportions differ significantly....

Use the sample data
below to test the hypotheses
:
: Not all population
proportions are the same
Populations
Response
1
2
3
Yes
200
200
91
No
150
200
109
where is the
population proportion of yes responses for population . Using a
level of significance 0.05.
The p-value is -
Select your answer -less than .005between .005 and .01between .01
and .025between .025 and .05between .05 and .10greater than .10
What is your
conclusion?
- Select your answer...

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...

Use the sample data below to test the hypothese. H0: p1=p2=p3.
Ha: Not all population proportions are the same.
Population 1: yes 150 no 100. Population 2: yes 150 no 150.
Population 3 yes 97 no 103.
Where Pi is the population proportion of yes responses for
population i. Using a .05 level of significance the
p-value=____?

Test the following hypotheses by using the χ 2
goodness of fit test.
H 0:
p A = 0.2, p B = 0.4,
and p C = 0.4
Ha:
The population proportions are not
p A = 0.2 , p B = 0.4 ,
and p C = 0.4
A sample of size 200 yielded 40 in category A, 120 in category
B, and 40 in category C. Use = .01 and test to see
whether the proportions are as stated...

In a quality control test of parts manufactured at Dabco
Corporation, an engineer sampled parts produced on the first,
second, and third shifts. The research study was designed to
determine if the population proportion of good parts was the same
for all three shifts. Sample data follow.
Production Shifts
Quality
First
Second
Third
Good
285
368
176
Defective
15
32
24
b. If the conclusion is that the population
proportions are not all the same, use a multiple comparison
procedure...

In a quality control test of parts manufactured at Dabco
Corporation, an engineer sampled parts produced on the first,
second, and third shifts. The research study was designed to
determine if the population proportion of good parts was the same
for all three shifts. Sample data follow.
Production Shift
Quality
First
Second
Third
Good
285
368
176
Defective
15
32
24
b. If the conclusion is that the population
proportions are not all the same, use a multiple comparison
procedure...

est the following hypotheses by using the χ 2
goodness of fit test.
H 0:
p A = 0.4, p B = 0.2,
and p C = 0.4
Ha:
The population proportions are not
p A = 0.4 , p B = 0.2 ,
and p C = 0.4
A sample of size 200 yielded 50 in category A, 120 in category
B, and 30 in category C. Use = .01 and test to see
whether the proportions are as stated...

Consider the following competing hypotheses and accompanying
sample data. Use Table 1.
H0 : P1−
P2 = 0.20
HA : P1−
P2 ≠ 0.20
x1 = 150
x2 = 130
n1 = 250
n2 = 400
a.
Calculate the value of the test statistic. (Round
intermediate calculations to at least 4 decimal places and final
answer to 2 decimal places.)
Test statistic
b.
Approximate the p-value.
p-value < 0.01
0.01 ≤ p-value < 0.025
0.025 ≤ p-value < 0.05...

A multinomial experiment produced the following results (Use
Table 3):
Category
1
2
3
4
5
Frequency
62
58
65
70
70
a.
Choose the appropriate alternative hypothesis to test if the
population proportions differ.
All population proportions differ from 0.20.
Not all population proportions are equal to 0.20.
b.
Calculate the value of the test statistic.
(Round intermediate calculations to 4
decimal places and your final answer to 2 decimal
places.)
χ2df
c.
Specify the decision rule...

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