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Confidence Intervals for a Mean (Lesson 8.6)

Chapter 8 - Day 8

Learning Targets
  • Use sample data to check the Normal/Large Sample condition.

  • Use the four-step process to construct and interpret a confidence interval for a population mean.

Activity: How Many States Can You Name?
Four-Step Template

Experience First

Another fun Activity today! Students will be writing down as many states as they can in 60 seconds. We remind students that abbreviations don't count (Michigan, not MI) and spelling doesn't matter. If any of your students get 25+, have them sing the song for the class. At the completion of the 60 seconds, they count up their states and record the number on the board. 

Students will enter the data into the 1 Quantitative Variable, Single Group applet at

If your class size is less than 30, students will likely get stuck at the Normal/Large Condition. Tell students to continue with the full 4-step confidence interval and that you will address this concern in the debrief. See the hard way below. 

There are three potential ways to satisfy the Normal/Large Sample Condition. We tell students that they are easy, medium, and hard. 

Easy: If the population distribution is (approximately) normal, then the sampling distribution of the sample mean is (approximately) normal.

Medium: If the population distribution is not normal (or shape is unknown), the sampling distribution of the sample mean is approximately normal if the sample size is large enough, which is 30 in most cases. Students learned about the Central Limit Theorem in Lesson 7.5.

Hard: If the shape of the population is unknown and the sample size is small, graph the sample data. If the sample data shows no strong skewness and no outliers, it is reasonable to assume the population distribution is approximately normal (meaning the sampling distribution is approximately normal).

Formalize Later

Here are some tips for using the four-step process for inference:

  • Maintain high expectations for what students should be producing. Clearly communicate these expectations and hold them accountable when grading.

  • Establish patterns of thinking that will help students later. For example, always have students write a general formula first, followed by the specific formula, followed by numbers plugged in, and then a final answer. We will maintain this expectation for all confidence intervals and significance tests in Chapters 8-11.

  • Don’t reveal calculator commands or applets yet. Of course, all the work of today’s lesson can be done with TInterval on the TI 83/84 calculator or using the 1 Quantitative Variable, Single Group applet. It is important that students become very familiar with the formulas and process for creating an interval. At the end of the chapter we will reveal the calculator commands for confidence intervals (a good way for them to check their final answers). 

We suggest you allow students to use the four-step templates for all homework questions. You will have to then decide whether or not they get templates for quizzes and tests. We allow templates for the quizzes, but not the test.  

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