A research institute poll asked respondents if they felt vulnerable to identity theft. In the poll, n=929 and x=523 who said "yes". Use a 99% confidence level.

a. Find the best point estimate of the population P. (Round to three decimal places as needed)
b. Identify the value of margin of error E. (Round to four decimal places as needed)
c. Construct a confidence interval. ___ < p <. (Round to three decimal places as needed)
d. Write a statement that correctly interprets the confidence interval. Choose the correct answer bellow

1. One has 99% conficence that the interval from the lower bound to the upper boundactually does contain the true value of the population proportion.
2. 99% of sample proportions will fall between the lower bound and the upper bound.
3. there is a 99% chance that the true value of the population proportion will fall between the lower bound and the upper bound.
4. One has 99% confidence that the sample proportion is equal to the population proportion

Step-by-step explanation:

Hello!

The variable of interest is

X: Number of people that feel vulnerable to identity theft in a sample of 929.

This variable is discrete and has a binomial distribution. X~Bi(n;p)

The parameter of interest is the population proportion of people that feel vulnerable to identity theft.

To calculate the 99% CI for the population proportion you have to use the approximate distribution to normal for the sample proportion p'≈N(p; )

a. The best point estimate for p is the sample proportion p' you calculate it as:

p'= x/n= 523/929= 0.56

b. The formula for the confidence interval is

p' ±

Where is the margin of error

In this case

c. Then the interval is

0.56 ± 0.04

[0.52;0.6]

d.

With a 99% confidence level, you can expect that the interval [0.52;0.6] will include the true value of the proportion of people that feel vulnerable to identity theft.

The correct answer is

3. there is a 99% chance that the true value of the population proportion will fall between the lower bound and the upper bound.

I hope this helps!