(Old) Math 101 — Lectures

Ch 16.1, 16.2 & 16.3 — Confidence Intervals

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Most of the important concepts in this chapter are in Ch 16.2 and 16.3. There is a lot of overlapping in these two chapters.

 

Statistical inference — Confidence Intervals (Ch 16.1, 16.2)

https://youtu.be/oyDZth6u2iY

 

The reasoning behind confidence intervals (Ch 16.1, 16.2)

https://youtu.be/8SQgROUkoAY

 

Example

https://youtu.be/Q_r1-J19MfU

The example in the video shows how to construct a 95% confidence interval by using z = 2 from the 3-number rule. But if we want to construct a confidence interval with a different middle area e.g. a 87% confidence interval, then we need to look up the z table directly to get the corresponding z value. The details are in the Classwork video below.

 

Confidence Interval Formula (Ch 16.3)

https://youtu.be/FAxteeOuVKg

 

Classwork

— Two classwork problems to turn in by the due date:

# 16.19 a) only          (in Exercises at the end of the chapter)

#16.6                          (in Ch 16.3 Section Apply Your Knowledge)

The video below shows you how to do #16.19 a). You follow the same format and write out your answer for #16.19a). Then use that format to do #16.6 as that’s how the grader grades your Classwork.

https://youtu.be/YF66lhtcEpI

(No need to copy the questions, just write out your answers including the diagrams.)

 

Interpretation of a Confidence Interval

Think about your confidence level as a success rate of estimating \( \overline{x} \).

For example, a 80% confidence level means that your estimate is correct 80% of the time. Of course, a higher success rate is always better but it comes with a price! We will explore that in our homework.

You don’t need the following for Classwork. When you do your multiple choice homework, the following explanation will help.

ch16_2_interpretation

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