Conceptual self-assessment for: Better Understanding Statistical Inference by Estimating the Mean and its Confidence Intervals

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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.

Question 1

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 Z_{\alpha/2} and t_{\alpha/2, n-1} 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?

Question 2

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.

If you’re one of my students, then you’re expected to answer these on your own and submit them according to the directions provided in class, i.e. you don’t  need to submit them through this website. Don’t forget that our TA and I are both here to help you in the associated lab (and/or tutorial) sessions.

Aim to provide succinct answers to these applications questions in the same document you created for the conceptual self-assessment questions.

I’d also like you to submit an Excel spreadsheet along with that document. This will likely require a bit of thoughtful organization on your part. For example, It would work well to put the answers to both of the above application problems onto their own sheet / tab within your spreadsheet, and name it accordingly. And then you can refer to that specific tab from your written document.

When you answer other applied question sets in future topics, you should do the calculations on separate sheets / tabs, also appropriately named. And refer to them where required to show your work. This way, you’ll have all of your Excel work in one nicely indexed place and will only need to hand in a single spreadsheet as an appendix to each set of self-assessments.

You can click through to other self-assessments or lessons (if any) using the button below, and return here whenever you wish.

The following schedules are for Alex’s in-class students:

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