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a newsgroup is interested i nterval for the proportion avor of a new Green initia elected Americans surveye

a newsgroup is interested i nterval for the proportion avor of a new Green initia elected Americans surveye

Holt Mcdougal Larson Pre-algebra: Student Edition 2012
Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter11: Data Analysis And Probability
Section: Chapter Questions
Problem 8CR
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A newsgroup is interested in constructing a 95% confidence interval for the proportion of all Americans who are in favor of a new Green initiative. Of the 585 randomly selected Americans surveyed, 355 were in favor of the initiative. Round answers to 2 decimal places where possible. a. With 95% confidence the proportion of all Americans who favor the new Green initiative is between and b. If many groups of 585 randomly selected Americans were surveyed, then a different confidence interval would be produced from each group. About percent of these confidence intervals will contain the true population proportion of Americans who favor the Green initiative and about percent will not contain the true population proportion.
Transcribed Image Text:A newsgroup is interested in constructing a 95% confidence interval for the proportion of all Americans who are in favor of a new Green initiative. Of the 585 randomly selected Americans surveyed, 355 were in favor of the initiative. Round answers to 2 decimal places where possible. a. With 95% confidence the proportion of all Americans who favor the new Green initiative is between and b. If many groups of 585 randomly selected Americans were surveyed, then a different confidence interval would be produced from each group. About percent of these confidence intervals will contain the true population proportion of Americans who favor the Green initiative and about percent will not contain the true population proportion.
Expert Solution
Step 1

Given,

sample size(n)  =585

x = number of Americans who are in favor of the Green initiative = 355

sample proportion (p^) = x/n  = 355/585 = 0.6068

significance level (α) = 0.05
For 95 % confidence level ,Zα/2 = 1.96

Margin of error (E) = Zα/2*√p^*(1-p^)/n

                              = 1.96*√0.6068*(1-0.6068)/585

                              = 0.0396

a) The 95% confidence interval for the proportions of all Americans who favor the new Green initiative
= p^  ± Margin of error
= 0.6068± 0.0396
=  (0.5672,0.6464)
≈ 0.57 < p< 0.65

The 95% confidence interval for the proportions of all Americans who favor the new Green initiative is between 0.57 and 0.65.

 

 

 

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