AP Statistics Section 10.1 C Determining Necessary Sample Size

Consider the confidence interval for the mean of a population where is known. In this formula, gives the margin of error. Ideally, we would like the margin of error to be small.

An equivalent expression for the margin of error is. This expression gets smaller when….

z * gets smaller. This happens when So there is a trade-off between the confidence level and the margin of error. To obtain a smaller margin of error from the same data you must be willing to accept lower confidence.

gets smaller. This can’t happen though - is a fixed value from the population.

n gets larger. Now this is something that we can control. For example, in order to cut the margin of error in half, we need to a sample size that is ______ times as large.

A wise user of statistics, which we of course are, never plans data collection without planning the inference at the same time. To determine the sample size n that will yield a confidence interval for a population mean with a specified margin of error, m, set the expression for the margin of error to be less than or equal to m and solve for n.

Example: Researchers would like to estimate the mean cholesterol level of a particular variety of monkey that is often used in laboratory experiments. They would like their estimate to be within 1 mg/dcl of blood of the true value of at a 95% confidence level. A previous study involving this variety of monkey suggests that the standard deviation of cholesterol level is about mg/dcl. What is the minimum number of monkeys needed to generate a satisfactory estimate?

Always round up to the next whole number when finding n.

It is the size of the sample that determines the margin of error. The size of the population does not influence the sample size we need - as long as the population is at least 10 times as large as the sample.