Question: Explaining confidence The admissions director from Big City University found that (107.8, 116.2) is a 95% confidence interval for the mean IQ score of all freshmen. Discuss whether each of the following explanations is correct.
(a) There is a 95% probability that the interval from 107.8 to 116.2 contains m.
(b) There is a 95% chance that the interval (107.8, 116.2) contains x.
(c) This interval was constructed using a method that produces intervals that capture the true mean in 95% of all possible samples.
(d) If we take many samples, about 95% of them will contain the interval (107.8, 116.2).
(e) The probability that the interval (107.8, 116.2) captures m is either 0 or 1, but we don't know which.