Researchers planning a study of the reading ability of third-grade children want to obtain a 95% confidence interval for the population mean score on a reading test, with margin of error no greater than 3 points. They carry out a small pilot study to estimate the variability of test scores. The sample standard deviation is s = 12 points in the pilot study, so in preliminary calculations the researchers take the population standard deviation to be sigma equals 12.

a) The study budget will allow as many as 100 students. Calculate the margin of error of the 95% confidence interval for the population mean based on n = 100.
b) There are many other demands on the research budget. If all of these demands were met, there would be funds to measure only 10 children. What is the margin of error of the confidence interval based on n = 10 measurements?
c) Find the smallest value of n that would satisfy the goal of a 95% confidence interval with margin of error 3 or less. Is this sample size within the limits of the budget?