Show that a ( 1 − α ) level confidence interval for the difference between two populationproportions that has a margin of error of at most E can be obtainedby choosing n 1 = n 2 = ( p ^ 1 g ( 1 − p ^ 1 g ) ) + ( p ^ 2 g ( 1 − p ^ 2 g ) ) ( z α 2 E ) 2 or not.

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Answer 1

Question

Chapter 12.3, Problem 134E

a.

To determine

Show that a (1−α) level confidence interval for the difference between two populationproportions that has a margin of error of at most E can be obtainedby choosing n1=n2=(p^1g(1−p^1g))+(p^2g(1−p^2g))(zα2E)2 or not.

b.

To determine

Explain why the formula in part (a) yields smaller sample sizes than the formula in exercise 12.133.

c.

To determine

Explain why choosing the sample sizes using the formula in part (a) is preferable than choosing the sample sizes using the formula in exercise 12.133.

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Answer 2

Question

Chapter 12.3, Problem 134E

a.

To determine

Show that a (1−α) level confidence interval for the difference between two populationproportions that has a margin of error of at most E can be obtainedby choosing n1=n2=(p^1g(1−p^1g))+(p^2g(1−p^2g))(zα2E)2 or not.

b.

To determine

Explain why the formula in part (a) yields smaller sample sizes than the formula in exercise 12.133.

c.

To determine

Explain why choosing the sample sizes using the formula in part (a) is preferable than choosing the sample sizes using the formula in exercise 12.133.

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Answer 3

Question

Chapter 12.3, Problem 134E

a.

To determine

Show that a (1−α) level confidence interval for the difference between two populationproportions that has a margin of error of at most E can be obtainedby choosing n1=n2=(p^1g(1−p^1g))+(p^2g(1−p^2g))(zα2E)2 or not.

b.

To determine

Explain why the formula in part (a) yields smaller sample sizes than the formula in exercise 12.133.

c.

To determine

Explain why choosing the sample sizes using the formula in part (a) is preferable than choosing the sample sizes using the formula in exercise 12.133.

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Answer 4

Question

Chapter 12.3, Problem 134E

a.

To determine

Show that a (1−α) level confidence interval for the difference between two populationproportions that has a margin of error of at most E can be obtainedby choosing n1=n2=(p^1g(1−p^1g))+(p^2g(1−p^2g))(zα2E)2 or not.

b.

To determine

Explain why the formula in part (a) yields smaller sample sizes than the formula in exercise 12.133.

c.

To determine

Explain why choosing the sample sizes using the formula in part (a) is preferable than choosing the sample sizes using the formula in exercise 12.133.

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Answer 5

Chapter 12.3, Problem 134E

a.

To determine

Show that a (1−α) level confidence interval for the difference between two populationproportions that has a margin of error of at most E can be obtainedby choosing n1=n2=(p^1g(1−p^1g))+(p^2g(1−p^2g))(zα2E)2 or not.

b.

To determine

Explain why the formula in part (a) yields smaller sample sizes than the formula in exercise 12.133.

c.

To determine

Explain why choosing the sample sizes using the formula in part (a) is preferable than choosing the sample sizes using the formula in exercise 12.133.

Answer 6

Chapter 12.3, Problem 134E

a.

To determine

Show that a (1−α) level confidence interval for the difference between two populationproportions that has a margin of error of at most E can be obtainedby choosing n1=n2=(p^1g(1−p^1g))+(p^2g(1−p^2g))(zα2E)2 or not.

Answer 7

Chapter 12.3, Problem 134E

a.

To determine

Show that a (1−α) level confidence interval for the difference between two populationproportions that has a margin of error of at most E can be obtainedby choosing n1=n2=(p^1g(1−p^1g))+(p^2g(1−p^2g))(zα2E)2 or not.

Answer 8

b.

To determine

Explain why the formula in part (a) yields smaller sample sizes than the formula in exercise 12.133.

Answer 9

b.

To determine

Explain why the formula in part (a) yields smaller sample sizes than the formula in exercise 12.133.

Answer 10

c.

To determine

Explain why choosing the sample sizes using the formula in part (a) is preferable than choosing the sample sizes using the formula in exercise 12.133.

Answer 11

c.

To determine

Explain why choosing the sample sizes using the formula in part (a) is preferable than choosing the sample sizes using the formula in exercise 12.133.

Answer 12

Expert Solution & Answer

Answer 13

Expert Solution & Answer

Answer 14

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Answer 15

Ch. 12.1 - Why is statistical inference generally used to...Ch. 12.1 - Prob. 3E Ch. 12.1 - Prob. 4E Ch. 12.1 - Regarding a sample proportion: a. What is it? b....Ch. 12.1 - Regarding the phrase number of successes: a. For...Ch. 12.1 - For what is the phrase number of failures an...Ch. 12.1 - Explain the relationships among the sample...Ch. 12.1 - Prob. 9E Ch. 12.1 - Repeat parts (b)(e) of Exercise 12.9 for samples...Ch. 12.1 - Prob. 11E

Show that a ( 1 − α ) level confidence interval for the difference between two populationproportions that has a margin of error of at most E can be obtainedby choosing n 1 = n 2 = ( p ^ 1 g ( 1 − p ^ 1 g ) ) + ( p ^ 2 g ( 1 − p ^ 2 g ) ) ( z α 2 E ) 2 or not.

Solution Summary: The author demonstrates that a level confidence interval for the difference between two populationproportions with at most E can be obtained.

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Show that a (1−α) level confidence interval for the difference between two populationproportions that has a margin of error of at most E can be obtainedby choosing n1=n2=(p^1g(1−p^1g))+(p^2g(1−p^2g))(zα2E)2 or not.

Explain why the formula in part (a) yields smaller sample sizes than the formula in exercise 12.133.

Explain why choosing the sample sizes using the formula in part (a) is preferable than choosing the sample sizes using the formula in exercise 12.133.

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Chapter 12 Solutions