Question

In a recent telephone survey, 5,000 randomly selected teenagers were asked to cite their primary social network site. Six of 10 teenagers said they use Mybook as their primary social network site. A 95% confidence interval to estimate the true proportion of teenagers who use Mybook as their primary social network site is found to be (0.2964, 0.9036). Which of the following is a correct interpretation of the confidence level?

Ninety-five percent of all samples of this size would yield a confidence interval of (0.2964, 0.9036).

There is a 95% chance that the true proportion of teenagers who use Mybook as their primary social network site is in the interval (0.2964, 0.9036).

Ninety-five percent of the time, the procedure used to generate this interval will capture the true proportion of teenagers who use Mybook as their primary social network site.

Ninety-five percent of all the samples of size 5,000 lie in the confidence interval (0.2964, 0.9036).

There is a 95% chance that randomly selected teenagers will be part of the 60% who use Mybook as their primary social network site.

Answer 1

The correct interpretation is that 95% of the time, the procedure used to generate this interval will capture the true proportion of teenagers who use Mybook as their primary social network site. It is not a probability of samples or a guarantee for a specific set of data, but rather a measure of the estimation process's reliability.

Step-by-step explanation:

The correct interpretation of the 95% confidence level in the context of the survey is that 95% of the time, the procedure used to generate this interval will capture the true proportion of teenagers who use Mybook as their primary social network site. It is not correct to interpret it as meaning that there is a 95% chance that the true proportion is within the interval for a given sample or that a specific percentage of all samples lie within the interval.

Statistical confidence intervals provide an estimate range of where the true proportion or mean of the entire population is located, based on the sample data. In this case, we are saying that we are 95% confident that the true proportion of all teenagers that prefer Mybook falls between 0.2964 and 0.9036.

It is important to note that a confidence interval does not imply that there is a 95% chance that any new sample taken will fall within the provided range. Instead, it's about the reliability of the estimation process over many samples.

Answer 2

Ninety-five percent of the time, the procedure used to generate this interval will capture the true proportion of teenagers who use Mybook as their primary social network site.

Step-by-step explanation:

Took the test