Question

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 = 1033 ) and ( x = 593 ) who said \yes.\ use a ( 95% ) confidence level.
click the icon to view a table of z scores.
c) construct the confidence interval.
( 0.544 < p < 0.604 )
(round to three decimal places as needed.)
d) write a statement that correctly interprets the confidence interval. choose the correct answer below.
a. ( 95% ) of sample proportions will fall between the lower bound and the upper bound.
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 interval from the lower bound to the upper bound actually does contain the true value of the population proportion.
d. one has ( 95% ) confidence that the sample proportion is equal to the population proportion.

Explanation:

d) Step1: Understand confidence interval interpretation

A confidence interval gives a range of values within which the population proportion is likely to lie. A 95% confidence interval means that if we were to take many samples and construct confidence intervals, about 95% of those intervals would contain the true population proportion.

d) Step2: Analyze each option

• Option A: Incorrect. It's about the population proportion being in the interval, not sample proportions.
• Option B: Incorrect. It's not about chance for a single constructed interval.
• Option C: Correct. A 95% confidence interval implies that we are 95% confident that the interval actually contains the true value of the population proportion.
• Option D: Incorrect. The sample proportion is just an estimate, and the confidence interval is about the population proportion.

Answer:

C. 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.