Which of the following statements is(are) correct concerning a 95% confidence interval?

A)There is a 0.95 probability that the population parameter of interest is contained within the interval.

B)In computing confidence intervals from 20 samples, 19 of the intervals would contain the population mean.

C)If you were to produce all possible confidence intervals using the sample mean of each sample of a given size from the population, then 95% of the intervals would contain the population mean.
D)There is a 0.05 probability the population parameter of interest is not contained within theinterval.

Question

Which of the following statements is(are) correct concerning a 95% confidence interval?

A)There is a 0.95 probability that the population parameter of interest is contained within the interval.

B)In computing confidence intervals from 20 samples, 19 of the intervals would contain the population mean.

C)If you were to produce all possible confidence intervals using the sample mean of each sample of a given size from the population, then 95% of the intervals would contain the population mean.
D)There is a 0.05 probability the population parameter of interest is not contained within theinterval.

Quizplus · Accepted Answer

A common misconception is that a 95% confidence interval means there is a 95% probability that the interval contains the population parameter. This is incorrect because once the interval is calculated, the parameter is either in it or not; probability no longer applies in this context. The correct interpretation, as stated in option C, is that if we were to take many samples and construct a confidence interval from each, 95% of those intervals would contain the population parameter. Options A and D are incorrect because they misinterpret the meaning of confidence intervals in a probabilistic sense. Option B is incorrect because it implies a certainty about the number of intervals containing the mean from a fixed number of samples, which is not how confidence intervals work.

Which of the Following Statements Is(are) Correct Concerning a 95