\In a recent text message survey, 4,000 randomly selected teenagers were asked to cite their favorite Florida college football team. Twenty-two of 40 teenagers said the Florida Gators are their favorite team. A 99% confidence interval to estimate the true proportion of teenagers who like the Florida Gators is found to be (0.3474, 0.7526). Which of the following is a correct interpretation of the confidence level?

Answers: Ninety-nine percent of all samples of this size would yield a confidence interval of (0.3474, 0.7526).
There is a 99% chance that the true proportion of teenagers who like the Florida Gators is (0.3474, 0.7526).
Ninety-nine percent of all the samples of size 4,000 lie in the confidence interval (0.3474, 0.7526).
Ninety-nine percent of the time, the procedure used to generate this interval will capture the true proportion of teenagers who like the Florida Gators.
There is a 99% chance that randomly selected teenagers will be part of the 55% who like the Florida Gators.

Question

21-08-2022
Advanced Placement (AP)

contestada

\In a recent text message survey, 4,000 randomly selected teenagers were asked to cite their favorite Florida college football team. Twenty-two of 40 teenagers said the Florida Gators are their favorite team. A 99% confidence interval to estimate the true proportion of teenagers who like the Florida Gators is found to be (0.3474, 0.7526). Which of the following is a correct interpretation of the confidence level?

Answers: Ninety-nine percent of all samples of this size would yield a confidence interval of (0.3474, 0.7526).
There is a 99% chance that the true proportion of teenagers who like the Florida Gators is (0.3474, 0.7526).
Ninety-nine percent of all the samples of size 4,000 lie in the confidence interval (0.3474, 0.7526).
Ninety-nine percent of the time, the procedure used to generate this interval will capture the true proportion of teenagers who like the Florida Gators.
There is a 99% chance that randomly selected teenagers will be part of the 55% who like the Florida Gators.

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The correct interpretation of the confidence level is alternative: Ninety-nine percent of all the samples of size 4,000 lie in the confidence interval (0.3474, 0.7526).

What is a confidence level?

The confidence level represents the percentage of intervals that would include the population parameter if you sampled the same population over and over again. A 95% confidence level usually works well. This indicates that if you took a hundred samples, and you calculated 95% confidence intervals, you would expect approximately 95% of the intervals to contain the population parameter, such as the population mean.

With that said, the correct interpretation of the confidence level is that at x% confidence level , we say that x% of all samples possible of the mentioned size will fall between the calculated range. Therefore, The correct interpretation of the confidence level is alternative: Ninety-nine percent of all the samples of size 4,000 lie in the confidence interval (0.3474, 0.7526).

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