Margin of Error
S.IC.4 Use data from a sample survey to estimate a population mean or proportion; develop a margin of error.
What is margin of error?
Whether we use a sample, survey, or study, there is always the chance that we have some type of error. Aside from errors that humans make, there are also systematic, instrument, and random errors. Because of this, we have to be able to account for a certain amount of error. The margin of error will give the maximum expected difference between the sample result and the population parameter.
The mean of a sample may or may not be the mean of the population the sample was drawn from. The margin of error helps you find the interval in which the mean of the population is likely to be. The margin of error is based on the size of the sample and the confidence level desired.
A 95% confidence level means that the probability is 95% that the true population mean is within a range of values called a confidence interval. It also means that when you select many different large samples from the same population, 95% of the confidence intervals will actually contain the population mean.
A sample proportion p is the ratio x/n, where x is the number of times an event occurs in a sample of size n.
