Question

State whether each of the following changes would make a confidence interval wider or narrower.​ (Assume that nothing else​ changes.) a. Changing from a 95​% confidence level to a 90​% confidence level. b. Changing from a sample size of 25 to a sample size of 250. c. Changing from a standard deviation of 20 pounds to a standard deviation of 30 pounds.

Answer 1

A) Confidence Interval will become narrower. B) Confidence Interval will become narrower. C) Confidence Interval will become broader.

Explanation:

Confidence Interval is the probable range around sample statistic, in which the population parameter is expected to lie.

Confidence Level shows the average percentage level of confidence interval, expected to contain population parameter. Lower confidence level implies narrower Confidence Interval

Bigger sample size reduces margin error (sample statistic, population parameter difference). Parameter-statistic proximity implies: narrower confidence interval around statistic, expected to contain parameter.

Standard Deviation is a measure of dispersion, spread. So, higher standard deviation implies more spread & broader confidence interval.