Q. 26 Construct and interpret a 95%聽c... [FREE SOLUTION]

91影视

The Practice of Statistics for AP

David Moore,Daren Starnes,Dan Yates

$Math Studyset 91影视 Explanations$ Math

4th Edition 路 809 pages

ISBN: 9781319113339

Chapter 10: Q. 26 (page 625)

Construct and interpret a $95 %$ confidence interval for $p_{1} - p_{2}$ in Exercise $24$ . Explain what additional information the confidence interval provides.

Short Answer

Expert verified

We are $95 %$ confident that the proportion difference is between $0.0175$ and $0.3075$ .

Step by step solution

Given Information

Given

$x_{1} = 34$

$n_{1} = 80$

$x_{2} = 21$

$n_{2} = 80$

Explanation

The sample proportion is the number of successes divided by the sample size:

${\hat{p}}_{1} = \frac{x_{1}}{n_{1}} = \frac{34}{80} = 0.425$

${\hat{p}}_{2} = \frac{x_{2}}{n_{2}} = \frac{21}{80} = 0.2625$

For confidence level $1 - 伪 = 0.95$ , determine $z_{伪 / 2} = z_{0.025}$ using table II (look up $0.025$ in the table, the $z$ -score is then the found $z$ -score with opposite sign):

$z_{伪 / 2} = 1.96$

The endpoints of the confidence interval for $p_{1} - p_{2}$ are then:

localid="1650451236001" $({\hat{p}}_{1} - {\hat{p}}_{2}) - z_{伪 / 2} 路 \sqrt{\frac{{\hat{p}}_{1} (1 - {\hat{p}}_{1})}{n_{1}} + \frac{{\hat{p}}_{2} (1 - {\hat{p}}_{2})}{n_{2}}} = (0.425 - 0.2625) - 1.96 \sqrt{\frac{0.425 (1 - 0.425)}{80} + \frac{0.2625 (1 - 0.2625)}{80}} 鈮� 0.0175$

localid="1650451247912" $({\hat{p}}_{1} - {\hat{p}}_{2}) + z_{伪 / 2} 路 \sqrt{\frac{{\hat{p}}_{1} (1 - {\hat{p}}_{1})}{n_{1}} + \frac{{\hat{p}}_{2} (1 - {\hat{p}}_{2})}{n_{2}}} = (0.425 - 0.2625) + 1.96 \sqrt{\frac{0.425 (1 - 0.425)}{80} + \frac{0.2625 (1 - 0.2625)}{80}} 鈮� 0.3075$

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91影视

Construct and interpret a $95 %$ confidence interval for $p_{1} - p_{2}$ in Exercise $24$ . Explain what additional information the confidence interval provides.

Short Answer

Step by step solution

Given Information

Explanation

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91影视

Construct and interpret a 95%confidence interval for p1-p2 in Exercise 24. Explain what additional information the confidence interval provides.

Short Answer

Step by step solution

Given Information

Explanation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Theoretical and Mathematical Physics

Applied Mathematics

Pure Maths

Probability and Statistics

Statistics

Study anywhere. Anytime. Across all devices.

Construct and interpret a $95 %$ confidence interval for $p_{1} - p_{2}$ in Exercise $24$ . Explain what additional information the confidence interval provides.