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 = 923 and x= 580 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. 0.628 (Round to three decimal places as needed.) b) Identify the value of the margin of error E. E = 0.031 (Round to three decimal places es needed.) c) Construct the confidence interval. (Round to three decimal places as needed.)
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 = 923 and x= 580 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. 0.628 (Round to three decimal places as needed.) b) Identify the value of the margin of error E. E = 0.031 (Round to three decimal places es needed.) c) Construct the confidence interval. (Round to three decimal places as needed.)
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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![**Using Sample Data and Confidence Levels to Estimate Population Proportions**
A research institute conducted a poll to determine if respondents felt vulnerable to identity theft. The sample consisted of 923 individuals, of which 580 responded "yes." A 95% confidence level was used for this analysis.
### Calculations
**a) Best Point Estimate of the Population Proportion (p)**
The best point estimate for the population proportion is calculated as:
\[ p = \frac{x}{n} = \frac{580}{923} = 0.628 \]
*(Value rounded to three decimal places as needed.)*
**b) Margin of Error (E)**
The margin of error is the range within which we can expect the true population proportion to fall. It is given as:
\[ E = 0.031 \]
*(Value rounded to three decimal places as needed.)*
**c) Construct the Confidence Interval**
The confidence interval provides a range of values, calculated from the sample data, within which the true population proportion is expected to fall. Using the point estimate and margin of error, the confidence interval is constructed as:
\[ (\text{lower bound}, \text{upper bound}) = (p - E, p + E) \]
This simplifies to:
\[ (0.628 - 0.031, 0.628 + 0.031) \]
\[ (0.597, 0.659) \]
*(Values rounded to three decimal places as needed.)*
**Conclusion**
The estimated population proportion of individuals feeling vulnerable to identity theft is approximately 0.628, with a 95% confidence interval ranging from 0.597 to 0.659. The computed margin of error is 0.031.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1354c2fd-0b46-4042-9d11-8a5cc5c0a3a3%2F5c50cea0-757a-414e-a40e-550e51f7069e%2F9z5okya_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Using Sample Data and Confidence Levels to Estimate Population Proportions**
A research institute conducted a poll to determine if respondents felt vulnerable to identity theft. The sample consisted of 923 individuals, of which 580 responded "yes." A 95% confidence level was used for this analysis.
### Calculations
**a) Best Point Estimate of the Population Proportion (p)**
The best point estimate for the population proportion is calculated as:
\[ p = \frac{x}{n} = \frac{580}{923} = 0.628 \]
*(Value rounded to three decimal places as needed.)*
**b) Margin of Error (E)**
The margin of error is the range within which we can expect the true population proportion to fall. It is given as:
\[ E = 0.031 \]
*(Value rounded to three decimal places as needed.)*
**c) Construct the Confidence Interval**
The confidence interval provides a range of values, calculated from the sample data, within which the true population proportion is expected to fall. Using the point estimate and margin of error, the confidence interval is constructed as:
\[ (\text{lower bound}, \text{upper bound}) = (p - E, p + E) \]
This simplifies to:
\[ (0.628 - 0.031, 0.628 + 0.031) \]
\[ (0.597, 0.659) \]
*(Values rounded to three decimal places as needed.)*
**Conclusion**
The estimated population proportion of individuals feeling vulnerable to identity theft is approximately 0.628, with a 95% confidence interval ranging from 0.597 to 0.659. The computed margin of error is 0.031.
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