Question

Does a confidence interval get wider or narrower if: (a) the percent of desired confidence decreases from 95% to 90%? (b) the size of the sample used to produce the confidence interval is decreased?

Answer 1

Answer 2

(a) If the percent of desired confidence decreases from 95% to 90%, the confidence interval will get narrower. A higher confidence level (e.g., 95%) requires a wider interval to be more certain that the true population parameter is captured within the interval. On the other hand, a lower confidence level (e.g., 90%) allows for a narrower interval since there is less certainty required.

(b) If the size of the sample used to produce the confidence interval is decreased, the confidence interval will get wider. A larger sample size provides more information about the population, leading to a more precise estimate of the population parameter. With a smaller sample size, there is less information, resulting in a wider range of possible values for the parameter, leading to a wider confidence interval.

Answer 3

A 99 percent confidence interval would be wider than a 95 percent confidence interval (for example, plus or minus 4.5 percent instead of 3.5 percent). A 90 percent confidence interval would be narrower (plus or minus 2.5 percent, for example).