## Chapter 8 - Day 5 - Lesson 8.2

##### Learning Targets
• 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.

##### Activity: What proportion of the Earth is covered by water?

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 one on Amazon. Arrange students in a large circle and allow them to throw the globe to their classmates. Be sure they put some spin on each throw. 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.

##### The Four-Step Process

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 develop student inferential thinking, but it’s also no coincidence that it matches closely with the four-point rubrics for the free response questions on the AP Exam. 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.

##### Tips for Using the Four-Step Process
• 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 8-12.

• While it is important that students know how to check each condition, it is equally important that they understand why we check the condition. We call this the “so what?”.

• Random Condition: so we can generalize to the population.

• 10% Condition: so sampling without replacement is OK.

• Large Counts: so the sampling distribution of the sample proportions will be approximately Normal and we can use z* to do calculations.

• Don’t reveal calculator commands yet. Of course, all the work of today’s lesson can be done with 1-PropZInt on the TI 83/84 calculator. 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. Then we instruct students that they are to use this feature only to check their final answer on a Free Response question (or on a MC question if they wish).