Suppose that in planning a study you calculate the margin of

Suppose that in planning a study you calculate the margin of error and decide it is too large. You have three choices of actions to reduce it: 1) Use a lower level of confidence. 2) Choose a larger sample size. 3) Reduce the population standard deviation. Which of these would be the most appropriate and why?

Solution

to reduce the margin of error it is wiser to use a larger sample size. As we know lowering the level fo confidence means allowing a higher of chance of rejecting the true null hypothesis which bears serious consequences. And Population standard deviation is a parameter (most cases it isunkonwn) and hence uncontrollable. So, that effectively leaves us with one option that is enlarging the sample size. Doing so, we are also reducing the sample variance of the statistic(which is indeed good) and by taking a larger sample margin of error is effectively reduced.