Question

Complete the statements by filling in the blank. When constructing a confidence interval, to increase the level of confidence, you must ________ [increase/decrease] the margin of error and the confidence interval will be _________ [narrower/wider]. A larger sample size will improve the precision of the confidence interval, therefore, all things being equal, a larger sample size will result in a __________ [smaller/larger] margin of error and the confidence interval will be _________ [narrower/wider].

Answer 1

Increase; wider; smaller; narrower.

Explanation:

In Statistics, sampling can be defined as a process used to collect or select data (objects, observations, or individuals) from a larger statistical population using specific procedures.

A confidence interval can be defined as a measure of the number of times that a population parameter would be within a given set of data. Thus, it is an estimate of the uncertainty of a given statistical data.

When constructing a confidence interval, to increase the level of confidence, you must increase the margin of error and the confidence interval will be wider. A larger sample size will improve the precision of the confidence interval, therefore, all things being equal, a larger sample size will result in a smaller margin of error and the confidence interval will be narrower.

Hence, for an estimator to be consistent it must have both a small bias and small variance.