Question

Assume that you are constructing a confidence interval for the mean (sigma unknown). The first time you construct the interval, you work at the 95% level of confidence. Then you construct the interval on the basis of a 99% level of confidence - changing only the level of confidence. The shift from the 95% to the 99% level of confidence will:

a. increase the precision of the estimate
b. not affect the precision of the estimate
c. impossible to determine based on the information provided
d. decrease the precision of the estimate

Answer 1

The shift from a 95% to a 99% level of confidence will decrease the precision of the estimate.

Step-by-step explanation:

The shift from a 95% to a 99% level of confidence will decrease the precision of the estimate.

When constructing a confidence interval, a higher level of confidence means that we want to be more certain that the interval contains the true population parameter. In order to increase the level of confidence, we need to widen the interval, which decreases the precision of the estimate. Conversely, decreasing the level of confidence would result in a narrower interval and increased precision.