use the sample data and confidence level given below to complete parts (a) through (d). a research institute…

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 = 954 and x = 580 who said \yes.\ use a 99% confidence level. click the icon to view a table of z scores. (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 99% 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 99% confidence that the sample proportion is equal to the population proportion. c. 99% of sample proportions will fall between the lower bound and the upper bound. d. there is a 99% chance that the true value of the population proportion will fall between the lower bound and the upper bound.
Answer
Explanation:
Step1: Recall confidence - interval interpretation
A confidence interval gives a range of values within which the true population parameter is likely to lie. For a proportion, a 99% confidence interval means that if we were to take many samples and construct confidence intervals in the same way, 99% of those intervals would contain the true population proportion.
Step2: Analyze each option
- Option A: This is the correct interpretation of a confidence interval. We are 99% confident that the interval from the lower - bound to the upper - bound actually contains the true value of the population proportion.
- Option B: The sample proportion is a point estimate and is not equal to the population proportion. A confidence interval is used to estimate the population proportion, not to claim equality between the sample and population proportions.
- Option C: It's not about 99% of sample proportions falling between the bounds. It's about the true population proportion being in the interval.
- Option D: It's not a probability statement about the true value falling in the interval in the sense of a single - trial probability. We are 99% confident, not that there is a 99% chance in a single - trial sense.
Answer:
A. One has 99% confidence that the interval from the lower bound to the upper bound actually does contain the true value of the population proportion.