Which of the following statements best describes the uncertainty associated with a 95% confidence interval for a population proportion, computed from a simple random sample?

A. We don't know whether the particular confidence interval is successful or not, but 95% of researchers are happy using this type of interval.

B. The 95% confidence interval successfully captures the true population proportion; we just don't know where in the interval it may actually be.

C. We don't know whether the particular confidence interval is successful or unsuccessful, but the success rate of the confidence interval procedure over all possible samples that could have been drawn is 95%.

D. The confidence interval successfully captures 95% of the true values of the population proportion.

I'll give you a hint to help you make the selection:

A 95% confidence interval means that there is a 95% probability that the true population proportion lies within the confidence interval.

DEzef

B. The 95% confidence interval successfully captures the true population proportion; we just don't know where in the interval it may actually be.

The correct answer is B. The 95% confidence interval successfully captures the true population proportion; we just don't know where in the interval it may actually be.

To understand why this is the correct answer, let's first define what a confidence interval is. A confidence interval is a range of values that is constructed based on a sample statistic and is used to estimate an unknown population parameter. In this case, the population parameter is a population proportion.

When we calculate a confidence interval, we use a specific level of confidence, in this case, 95%. This means that if we were to repeat the sampling and confidence interval process many times, approximately 95% of those intervals would contain the true population proportion.

However, it's important to note that for any one particular confidence interval, we don't know if it includes the true population proportion or not. This is the uncertainty associated with the confidence interval. It's like saying we have a range of possible values where the true population proportion may lie, but we cannot say with certainty the exact value within that range.

So, statement B accurately describes the uncertainty associated with a 95% confidence interval for a population proportion.