In this post, we’ll introduce a new statistics term called the margin of error. Since a sample is used to represent a population, the sample’s results are expected to differ from what the result would have been if you had surveyed the entire population. This difference is called the margin of error. The smaller the margin of error, the closer the results of the sample are to what the result would have been if you had surveyed the entire population.

The definition of margin of error is: the maximum amount that the sample results are expected to differ from those of the actual population. In other words, the margin of error is the range of values below and above the average result for the sample. The average result for the entire population is expected to be within that range. The margin of error is the maximum expected difference between a population parameter and a sample statistic.

Let’s review for a moment. In previous posts we looked at confidence intervals for two situations. The first situation happens rarely and is the case where we know the population variance. More commonly we don’t know the population variance. In this case, we use the Student’s T distribution.

The more observations you have in your sample, the more certain you are of your prediction. That makes sense.

Margin of Error with a Known Population Variance

Margin of Error with an Unknown Population Variance

The true population mean falls in the interval defined by the sample mean plus and minus the margin of error. It’s better for us to have the smallest possible confidence interval. How can we do that? Higher sample sizes will decrease the margin of error. This is intuitive. The more data you have obtained, the more likely your prediction will be close. In other words, the more observations there are in the sample, the higher the chances of getting a good idea about the true mean of the entire population.

ChatGPT

In statistics, if my sample size was the size of the population, the margin of error would be zero. True or False?

ChatGPT responded with False. In statistics, the margin of error (ME) is a measure of the variability of an estimator. It represents the range in which the true population parameter falls with a certain level of confidence, usually 95% or 99%. The margin of error is calculated based on the sample size, the standard deviation of the population, and the level of confidence.

Having a sample size equal to the population size would give you a 100% sample, but it would not guarantee a zero margin of error. The margin of error depends on the variability of the population, not just the sample size. Even with a sample size equal to the population size, there can still be variability in the sample statistics and hence a non-zero margin of error.