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.

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.