Confidence Intervals for a Proportion (Lesson 8.4)
Chapter 8 - Day 5
Use the four-step process to construct and interpret a confidence interval for a population proportion.
Determine the sample size required to obtain a C% confidence interval for a population proportion with a specified margin of error.
Another fun Activity today! Students will be trying to estimate the proportion of the Earth that is covered by water. They will do this by taking random samples of locations on Earth and recording whether that location is water or land. To do this, borrow an old globe from the cranky social studies teacher, or order this inflatable globe on Amazon. Arrange students in a large circle and allow them to throw the globe to their classmates (with some spin for randomness). When a student catches the globe, the location at the very tip of their pinky finger is the randomly selected location. Record water or land. Be sure to sample at least 50 locations. Teacher Tip: The true proportion of Earth that is water is 71 percent.
You can also use RANDOM.ORG to choose random locations on the globe.
This is the first time that students will be required to use the four-step process of STATE, PLAN, DO, CONCLUDE. This structure was developed specifically to support and develop student inferential thinking. This structure will be used for all inference problems for the remainder of the course, so it is critical that students become familiar with the expectations.
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 1-PropZInt on the TI 83/84 calculator or using the One sample z interval for a proportion 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 that 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.