Please answer only part "D" ### Confidence Interval Analysis: Population Proportion**Objective:** Use sample data and a specified confidence level to determine and interpret the confidence interval for a population proportion.**Scenario:**A research institute conducted a poll asking respondents if they felt vulnerable to identity theft. In the poll, - $ n = 1048 $ respondents - $ x = 568 $ respondents said "yes."- Use a 95% confidence level.**Steps:**1. **Find the best point estimate of the population proportion $ p $.** \[ \hat{p} = \frac{x}{n} = \frac{568}{1048} = 0.542 \] *(Round to three decimal places as needed.)* 2. **Identify the value of the margin of error $ E $.** - Given: $ E = 0.030 $ \[ E = 0.030 \] *(Round to three decimal places as needed.)*3. **Construct the confidence interval.** \[ \hat{p} - E < p < \hat{p} + E \] \[ 0.542 - 0.030 < p < 0.542 + 0.030 \] \[ 0.512 < p < 0.572 \] *(Round to three decimal places as needed.)*4. **Write a statement that correctly interprets the confidence interval.** \[ \text{Choose the correct answer from the options below:} \] - **A:** 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. - **B:** There is a 95% chance that the true value of the population proportion will fall between the lower bound and the upper bound. - **C:** One has 95% confidence that the sample proportion is equal to the population proportion. - **D:** 95% of sample proportions will fall between the lower bound and the upper bound. The correct answer is **A**, which accurately reflects the concept of confidence intervals in statistics.This analysis helps quantify the uncertainty around the point estimate of the population proportion, providing a range within which the true population proportion is likely to fall with a specified

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= 1048 and x = 568 who said "yes." Use a 95% confidence level. E Click the icon to view a table of z scores. a) Find the best point estimate of the population proportion p. 0.542 (Round to three decimal places as needed.) b) Identify the value of the margin of error E. E= 0.030 (Round to three decimal places as needed.) c) Construct the confidence interval. 0.512

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= 1048 and x = 568 who said "yes." Use a 95% confidence level. E Click the icon to view a table of z scores. a) Find the best point estimate of the population proportion p. 0.542 (Round to three decimal places as needed.) b) Identify the value of the margin of error E. E= 0.030 (Round to three decimal places as needed.) c) Construct the confidence interval. 0.512

Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015

1st Edition

ISBN:9781680331141

Author:HOUGHTON MIFFLIN HARCOURT

Publisher:HOUGHTON MIFFLIN HARCOURT

Chapter11: Data Analysis And Displays

Section11.3: Shapes Of Distributions

Problem 14E

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Concept explainers

Magnitude

A vector is an element with both direction and magnitude. A vector is represented using an arrow, where the arrow represents the direction of the vector and its length is represented using the magnitude. The set of vectors in space is known as vector space. The vectors can be added, subtracted, multiplied, and divided in a vector space. The image below shows a vector AB.

Question

Please answer only part "D"

### Confidence Interval Analysis: Population Proportion

**Objective:** Use sample data and a specified confidence level to determine and interpret the confidence interval for a population proportion.

**Scenario:**
A research institute conducted a poll asking respondents if they felt vulnerable to identity theft. In the poll,
- $ n = 1048 $ respondents
- $ x = 568 $ respondents said "yes."
- Use a 95% confidence level.

**Steps:**

1. **Find the best point estimate of the population proportion $ p $.**

\[
\hat{p} = \frac{x}{n} = \frac{568}{1048} = 0.542
\]
*(Round to three decimal places as needed.)*

2. **Identify the value of the margin of error $ E $.**
- Given: $ E = 0.030 $
\[
E = 0.030
\]
*(Round to three decimal places as needed.)*

3. **Construct the confidence interval.**

\[
\hat{p} - E < p < \hat{p} + E
\]
\[
0.542 - 0.030 < p < 0.542 + 0.030
\]
\[
0.512 < p < 0.572
\]
*(Round to three decimal places as needed.)*

4. **Write a statement that correctly interprets the confidence interval.**
\[
\text{Choose the correct answer from the options below:}
\]
- **A:** 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.
- **B:** There is a 95% chance that the true value of the population proportion will fall between the lower bound and the upper bound.
- **C:** One has 95% confidence that the sample proportion is equal to the population proportion.
- **D:** 95% of sample proportions will fall between the lower bound and the upper bound.

The correct answer is **A**, which accurately reflects the concept of confidence intervals in statistics.

This analysis helps quantify the uncertainty around the point estimate of the population proportion, providing a range within which the true population proportion is likely to fall with a specified

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