The following are some recommended conceptual self-assessment questions for the lesson called Better Understanding Statistical Inference by Estimating the Mean and its Confidence Intervals. They’re intended for you to work through to test your own knowledge of the key concepts we covered there.
This topic was so important to helping you build an understanding of what’s really happening when we estimate a population parameter from a sample. The following question are meant to reinforce the key concepts.
a) What is a sampling distribution?
b) We started looking at the standard error way back in our topic on Summarizing Data and Estimating Population Parameters Using Descriptive Measures. Then in this topic we picked it up again and went a little deeper. In particular, I told you that the standard error is like a 68.26% confidence interval. Can you explain what that means?
c) With that context in mind, what does a confidence interval achieve for us? For example and to be more specific, if a situation calls for a 99% confidence interval then what are the terms and doing for you in the equations for the confidence interval given on pages 7 and 12 of my notes? (We talked about this when we looked at the examples on pages 6 and 7.)
d) When do you use the t-distribution?
As much as I want you to understand the fundamental concepts under the hood here, it’s also a practical reality that you will sometimes need to answer questions about the precision of your estimated statistical parameters in a hurry, e.g. on a quiz, in an exam setting, or when some data comes across your desk at work. As such, I want you to create your own super duper cheat sheet for confidence intervals of the mean. I started the work on pages 17 and 18 of my notes. I want you to finish it for all the cases in the table on page 3.
You can click through to other self-assessments or lessons (if any) using the button below, and return here whenever you wish.