For the statements below,which is(are)TRUE for confidence intervals?
I As the percentage confidence increases,the confidence interval range decreases.
II Confidence intervals are calculated using the calculated mean and standard deviation of a set of n measurements;and the results of the F test.
III The 95% confidence interval will include the true population mean for 95% of the sets of n measurements.
A)I only
B)II only
C)I and III
D)I and II
E)III only

Question

Quizplus · Accepted Answer

Confidence intervals are calculated using the sample mean, standard deviation, and the critical value from a distribution (often the t-distribution for small samples or z-distribution for large samples), not the F test. As the percentage confidence increases, the confidence interval range actually increases because you're more confident that the interval contains the true mean, thus needing a wider range to capture this certainty. The statement about the 95% confidence interval is a common misunderstanding; it means that if we were to take many samples and construct a 95% confidence interval from each, 95% of those intervals would contain the true population mean, not that a single interval has a 95% chance of containing the mean.

For the Statements Below,which Is(are)TRUE for Confidence Intervals