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, $n=937$ and $x=513$ who said "yes." Use a $99 \%$ confidence lev
Click the icon to view a table of $z$ scores.
a) Find the best point estimate of the population proportion $p$.
547
(Round to three decimal places as needed.)
b) Identify the value of the margin of error $E$.
$E=.042$
(Round to three decimal places as needed.)
c) Construct the confidence interval.
$< p< $
(Round to three decimal places as needed.)
Answer
\(\boxed{0.547}\) is the best point estimate of the population proportion $p$.
Step 1 ：Given that the number of respondents who said 'yes' is $x = 513$ and the total number of respondents is $n = 937$.
Step 2 ：The best point estimate of the population proportion $p$ is given by the formula $p = \frac{x}{n}$.
Step 3 ：Substituting the given values into the formula, we get $p = \frac{513}{937}$.
Step 4 ：Calculating the above expression, we find that $p \approx 0.547$.
Step 5 ：\(\boxed{0.547}\) is the best point estimate of the population proportion $p$.
