Suppose a 95% confidence interval for μ turns out to be (1,000, 2,100). Give a definition of what it means to be "95% confident" in an inference.
A) In repeated sampling, the population parameter would fall in the given interval 95% of the time.
B) In repeated sampling, 95% of the intervals constructed would contain the population mean.
C) 95% of the observations in the entire population fall in the given interval.
D) 95% of the observations in the sample fall in the given interval.

Question

Quizplus · Accepted Answer

Being "95% confident" in an inference means that in repeated sampling, 95% of the intervals constructed would contain the population mean, which is described by option B. Option A is incorrect because we cannot make a statement about the population parameter with only one interval. Option C is incorrect because we cannot make a statement about the entire population with only one interval. Option D is incorrect because we are making an inference about the population mean, not the observations in the sample.

Suppose a 95% Confidence Interval for μ Turns Out to Be