Consider calculating a 95% confidence interval for a population mean $\mu$ based on a sample from a population, and then a 95% confidence interval for a population proportion p based on another sample selected independently from the same population. Which of the following statements are true?
A) Prior to obtaining data, the probability that the first interval will include $\mu$
Is )95.
B) Prior to obtaining data, the probability that the second interval will include p is .95.
C) The probability that both intervals will include the values of the respective parameters is about .90.
D) All of the above statements are correct.

Question

Quizplus · Accepted Answer

Each statement reflects the correct interpretation of confidence intervals. Prior to obtaining data, the probability that a 95% confidence interval will include the true parameter (mean $\mu$ or proportion $p$) is 0.95. The probability that both intervals include their respective true parameters is not directly calculated as a simple product (which would suggest 0.9025), but the conceptual understanding of confidence intervals supports the idea that each interval is constructed to include its true parameter 95% of the time, hence all statements are considered correct in the context of confidence interval interpretation.

Consider Calculating a 95% Confidence Interval for a Population Mean μ\muμ

Consider Calculating a 95% Confidence Interval for a Population Mean $\mu$