Question

Use the sample data and confidence level given below to complete parts (a) through (d). A research institute poll asked respondents if they felt vulnerable to identity theft. In the poll, n = 1045 and x = 519 who said "yes." Use a 95% 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. < p < (Round to three decimal places as needed.) d) Write a statement that correctly interprets the confidence interval. Choose the correct answer below. A. There is a 95% chance that the true value of the population proportion will fall between the lower bound and the upper bound. B. One has 95% confidence that the sample proportion is equal to the population proportion. C. 95% of sample proportions will fall between the lower bound and the upper bound. D. One has 95% confidence that the interval from the lower bound to the upper bound actually does contain the true value of the population proportion.

          Use the sample data and confidence level given below to complete parts (a) through (d).
A research institute poll asked respondents if they felt vulnerable to identity theft. In the poll, n = 1045 and x = 519 who said "yes." Use a 95% 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.
< p <
(Round to three decimal places as needed.)
d) Write a statement that correctly interprets the confidence interval. Choose the correct answer below.
A. There is a 95% chance that the true value of the population proportion will fall between the lower bound and the upper bound.
B. One has 95% confidence that the sample proportion is equal to the population proportion.
C. 95% of sample proportions will fall between the lower bound and the upper bound.
D. One has 95% confidence that the interval from the lower bound to the upper bound actually does contain the true value of the population proportion.

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Use the sample data and confidence level given below to complete parts (a) through (d).
A research institute poll asked respondents if they felt vulnerable to identity theft. In the poll, n = 1045 and x = 519 who said "yes." Use a 95% 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.
< p <
(Round to three decimal places as needed.)
d) Write a statement that correctly interprets the confidence interval. Choose the correct answer below.
A. There is a 95% chance that the true value of the population proportion will fall between the lower bound and the upper bound.
B. One has 95% confidence that the sample proportion is equal to the population proportion.
C. 95% of sample proportions will fall between the lower bound and the upper bound.
D. One has 95% confidence that the interval from the lower bound to the upper bound actually does contain the true value of the population proportion.

Added by Maureen H.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

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Solved by Expert David Nguyen

06/30/2022

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Use the following data and conclude the given correlation purpose: According to a research institute, 1045 out of 519 respondents said they felt vulnerable to identity theft. The confidence level used was 95%. Click the "Met table" to find the correlation. Find the population proportion. (Round to three decimal places if needed) Identify the value of the margin error. (Round to three decimal places if needed) Construct the confidence interval. (Round to three decimal places as needed) Write a statement that correctly interprets the confidence interval. Choose the correct answer based on the options below. There is a 95% chance that the interval value of the population proportion will be between the lower bound and the upper bound. One has 95% confidence that the sample proportion equals the population proportion. 95% of sample proportions will fall between the lower bound and the upper bound. One has 95% confidence that the interval from the lower bound to the upper bound actually contains the true value of the population proportion.

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00:01 Hi, i'm david and i'm here to help you and answer your question.

00:03 In the question here, we are going to discuss about the confidence interval for the proportion, the formula for the competence interval for the p.

00:12 It will be the sample proportion p hod plus and minus the merging of the error, where the p ht equal to the x over n and the merging of the error equal to the z and 4 over 2 times when the square root of the p ht times 1 minus the p ht over the n in the question here, we are given the symbol says n equal to the 1 ,045, and we're given the x, it will equal to the 519 that will answer yes.

00:45 Here i want to find a point estimate for the p.

00:49 So from here we can find the best point estimate of b, it will equal to the p heart and equal to the x over n, equal to the 519 over the 1045.

01:09 So we have the 519, devonably 1045, equal to the 0 .4.

01:15 Here i need to write to the 3 decimal presence will be the 497.

01:20 The next step that's going to find the e.

01:23 To find the e, we need to find the critical value first, the z and 4 over 2.

01:29 Here we want to have under 95 % confidence and 5 % equal to the 5 %, divided by 2, equal to 2.

01:36 The 2 .5 % which is equal to the 025.

01:40 It will look up the z table at this value equal to 1 .96.

01:44 Therefore we have the merging of the error by this formula here and then we should get the zan4 over 2 times when the square root of the phe would be the 0 .97 times 1 minus 0497 over the end will be the 1 045 and if we will compare it we will have 1 045 taking the square root times 1 .96.

02:16 I will need to round the answer to the 3 decimal places...

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