We have calculated a 95% confidence interval and would prefer for our next confidence interval to have a smaller margin of error without losing any confidence. In order to do this, we can
I. change the z* value to a smaller number. II. take a larger sample.
III. take a smaller sample.
A) III only
B) I and II
C) I and III
D) II only
E) I only

Question

Quizplus · Accepted Answer

Taking a larger sample (option II) will not necessarily lead to a smaller margin of error if the population standard deviation remains the same. Changing the z* value (option I) would require changing the confidence level and could result in a loss of confidence. Therefore, the best choice is to keep the same confidence level and reduce the margin of error by changing the sample size (option III). Taking a larger sample will result in a smaller margin of error, assuming all other factors are constant.

We Have Calculated a 95% Confidence Interval and Would Prefer