Question

Consider the usual confidence interval for the mean of a normal population with known variance. What is the relationship between confidence and precision as measured by interval width?
A. For a fixed sample size, decreasing the confidence level has no effect on the precision
B. For a fixed sample size, decreasing the confidence level decreases the precision
C. For a fixed sample size, decreasing the confidence level increases the precision
D. None of the above

Answer 1

C. For a fixed sample size, decreasing the confidence level increases the precision

Confidence interval = Mean Z*

As confidence level increase, Z* value increase and hence the confidence interval get wider. Wider confidence interval means less precision. So, with increase in confidence level, precision decreases and vice versa.