Which is true about a 90% confidence interval based on a given sample? I. The interval contains 90% of the population.
II) Results from 90% of all samples will lie in this interval.
III) The interval is smaller than a 95% confidence interval would be.
A) None
B) I only
C) II only
D) III only
E) I and III

Question

Quizplus · Accepted Answer

III is correct because a 90% confidence interval is narrower (smaller) than a 95% confidence interval, as it is constructed to capture the central 90% of the distribution of possible sample means, rather than the central 95%. I is incorrect because the interval does not contain 90% of the population, but rather we are 90% confident that the true population parameter lies within the interval. II is incorrect because it's not that 90% of all samples will lie within this specific interval, but rather that if we were to take many samples and construct a confidence interval from each, about 90% of those intervals would contain the true population parameter.

Which Is True About a 90% Confidence Interval Based on a Given