3.3.D—Calculate the standard error and margin of error of a sample statistic for a confidence interval for a…

Calculate the standard error and margin of error of a sample statistic for a confidence interval for a population proportion, and estimate a given sample size from the margin of error.

• The standard error (SE) of a statistic is an estimate of the standard deviation of the sampling distribution of the statistic. The standard error of the sample proportion p is SE pp np 1 .
• The standard error quantifies the typical amount that a statistic will vary from the value of the corresponding population parameter.
• The margin of error of p is half the width of the confidence interval and is calculated as the critical value z times the standard error (SE) of p, which equals p 1 z n . p
• The formula for the margin of error (MOE) can be rearranged to solve for n, n zp p MOE 2  1 2 , the minimum sample needed to achieve a given margin of error. For this purpose, if p is not defined or unable to be calculated, use p=0.5 in order to find the upper bound for the sample size that will result in a given mar gin of error. Inference for Categorical Data: Proportions UNIT 3 90