Knowing the Central Limit Theorem, we are ready to make our first inference. By inference, we mean that we are using our sample to infer information about the population.
This is really what we wanted from the beginning of the course. We can’t actually find the average weight of all Americans, but if we find a sample average, we can find an approximation of the true average.
The first inference we will make is known as the Confidence Interval. Using the sample average, we can formulate a range of values in which we can say the true value is (at least with some certainty).
For example, if we take the weights from a sample of 250 Americans and find a sample mean of 175 pounds with a standard deviation of 25 pounds, let’s quickly find a confidence interval with a 90% certainty (also known as a confidence level).
This doesn’t give an exact number, but it gives us a good approximation.
Over the next few pages, we’ll look at how to find the confidence interval. In this lesson, we will focus on a single sample of quantitative data