In a survey of 2477 adults in a recent​ year, 1491 say they have made a New​ Year's resolution. Construct​ 90% and​ 95% confidence intervals for the population proportion. Interpret the results and compare the widths of the confidence intervals. The​ 90% confidence interval for the population proportion p is

College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter8: Sequences, Series, And Probability
Section8.7: Probability
Problem 7E: List the sample space of each experiment. Selecting a letter of the alphabet
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In a survey of 2477 adults in a recent​ year,
1491 say they have made a New​ Year's resolution.
Construct​ 90% and​ 95% confidence intervals for the population proportion. Interpret the results and compare the widths of the confidence intervals.
The​ 90% confidence interval for the population proportion p is
 
A researcher wishes to​ estimate, with
95​%
​confidence, the population proportion of adults who think Congress is doing a good or excellent job. Her estimate must be accurate within
3​%
of the true proportion.
​(a) No preliminary estimate is available. Find the minimum sample size needed.
​(b) Find the minimum sample size​ needed, using a prior study that found that
38​%
of the respondents said they think Congress is doing a good or excellent job.
​(c) Compare the results from parts​ (a) and​ (b).
​(a) What is the minimum sample size needed assuming that no prior information is​ available?
n=
 
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