Confidence Intervals

As we saw with the previous simulations, our sample mean can vary from sample to sample. While, in a simulation, we have the luxury of taking 10,000 samples, we cannot do that in the real world; it would be far too expensive and time-consuming. Typically, we are given only enough resources to gather one sample. So how can we be confident in the results of our sample? Is there any way we can account for this variability when reporting our sample mean?

The good news is that the CLT gives us an idea of the variance in our sample mean. We can apply the CLT and take sampling variability into account by using a confidence interval. More generally, a confidence interval is a range of values for a statistic (an example of a statistic is a sample mean) based on a distribution that has some degree of confidence of how likely it is to contain the true value for the mean. We are not always going to be calculating confidence intervals for just the sample mean; the idea applies...