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
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
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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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