You are designing a study to measure the extent to which students in your very large school district are planning to attend post-secondary school. You are trying to figure out how large a sample you need to be sure that your estimates are reasonably accurate (have modest-sized confidence intervals around the means). You remember from your evaluation course something about the relationship between the size of the sample and the size of that confidence interval.
23. If you double the sample sizeâ€”say from 200 to 400 studentsâ€”
b. Give me a sense of how large the change in the width of the confidence interval around the impact estimate will beâ€”for example, what is the order of magnitude of the change?