Use the sample data and confidence level given below to complete parts (a) through (d). research institute poll asked respondents if they felt vulnerable to identity theft. In the poll, n = 906 and x-581 who said "yes. " Use a90% confidence level Use the sample data and confidence level given below to complete parts (a) through (d).Aresearch institute poll asked respondents if they felt vulnerable to identity theft. In the poll, n=906 and x=561 who said "yes." Use a90% confidence level.Click the icon to view a table of z scores.a) Find the best point estimate of the population proportion p.(Round to three decimal places as needed.)b) Identify the value of the margin of error E.E=(Round to three decimal places as needed.)c) Construct the confidence interval.(Round to three decimal places as needed.)d) Write a statement that correctly interprets the confidence interval. Choose the correct answer below.OA. One has 90% confidence that the interval from the lower bound to the upper bound actually does contain the true value of thepopulation proportion.OB. There is a 90% chance that the true value of the population proportion will fall between the lower bound and the upper bound.OC. 90% of sample proportions will fall between the lower bound and the upper bound.O D. One has 90% confidence that the sample proportion is equal to the population proportion.

Use the sample data and confidence level given below to complete parts (a) through (d). research institute poll asked respondents if they felt vulnerable to identity theft. In the poll, n = 906 and x-581 who said "yes. " Use a 90% confidence level

Use the sample data and confidence level given below to complete parts (a) through (d). research institute poll asked respondents if they felt vulnerable to identity theft. In the poll, n = 906 and x-581 who said "yes. " Use a 90% confidence level

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.5: Comparing Sets Of Data

Problem 26PFA

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Question

Use the sample data and confidence level given below to complete parts (a) through (d).
Aresearch institute poll asked respondents if they felt vulnerable to identity theft. In the poll, n=906 and x=561 who said "yes." Use a
90% confidence level.
Click the icon to view a table of z scores.
a) Find the best point estimate of the population proportion p.
(Round to three decimal places as needed.)
b) Identify the value of the margin of error E.
E=
(Round to three decimal places as needed.)
c) Construct the confidence interval.
(Round to three decimal places as needed.)
d) Write a statement that correctly interprets the confidence interval. Choose the correct answer below.
OA. One has 90% confidence that the interval from the lower bound to the upper bound actually does contain the true value of the
population proportion.
OB. There is a 90% chance that the true value of the population proportion will fall between the lower bound and the upper bound.
OC. 90% of sample proportions will fall between the lower bound and the upper bound.
O D. One has 90% confidence that the sample proportion is equal to the population proportion.

Expert Solution

Step 1

$G i v e n, s a m p l e s i z e (n) = 906 n o . o f s u c c e s s e s (x) = 581 s a m p l e p r o p o r t i o n (\hat{p}) = \frac{x}{n} \hat{p} = \frac{581}{906} = 0.641 1 - \hat{p} = 1 - 0.641 = 0.359 α = 1 - 0.95 = 0.05 \frac{α}{2} = 0.025 Z_{0.025} = 1.96 (f r o m Z - t a b l e)$

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