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 = 1065 $ and $ x = 565 $ who said "yes." Use a 95% confidence level.a) Find the best point estimate of the population proportion $ p $.\[\text{(Round to three decimal places as needed.)}\]b) Identify the value of the margin of error $ E $.\[ E = \]\[\text{(Round to three decimal places as needed.)}\]c) Construct the confidence interval.\[< p <\]\[\text{(Round to three decimal places as needed.)}\]d) Write a statement that correctly interprets the confidence interval. Choose the correct answer 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. 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.

Name: Use the sample data and confidence level given below to complete part
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Description: 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 = 1065 $ and $ x = 565 $ who said "yes." Use a 95% con

From the provided information, Sample size (n) = 1065, x = 565 a) The best point estimate of the…

Answered: Use the sample data and confidence…

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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 = 1065 $ and $ x = 565 $ who said "yes." Use a 95% confidence level.

a) Find the best point estimate of the population proportion $ p $.

\[
\text{(Round to three decimal places as needed.)}
\]

b) Identify the value of the margin of error $ E $.

\[ E = \]

\[
\text{(Round to three decimal places as needed.)}
\]

c) Construct the confidence interval.

\[
< p <
\]

\[
\text{(Round to three decimal places as needed.)}
\]

d) Write a statement that correctly interprets the confidence interval. Choose the correct answer 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. 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.

Expert Solution

Step 1

From the provided information,

Sample size (n) = 1065, x = 565

The best point estimate of the population proportion is sample proportion.

Thus, the required sample proportion can be obtained as:

Step 2

Confidence level = 95%

The z value at 95% confidence level from the standard normal table is 1.96.

The required margin of error can be obtained as:

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