Significance Tests for a Proportion (Lesson 9.4)
Chapter 9 - Day 4
Learning Targets
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Use the four-step process to perform a one-sided significance test about a population proportion.
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Calculate the P-value for a two-sided significance test about a population proportion using Table A or technology.
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Use the four-step process to perform a two-sided significance test about a population proportion.
Four-Step Template
Experience First
There has been a lot of debate recently about whether or not different colors of Skittles actually taste different. We decided to try and find the truth by doing an experiment. Students were blindfolded and asked to identify the color of Skittles based only on their taste. We then performed a significance test to assess whether or not we had convincing evidence that students can taste the rainbow.
We have students work in pairs (one taster and one recorder) and have each student try 5 Skittles. The recorder simply records trials as correct or incorrect. We tell the recorder they should not tell the taster whether they are right or wrong for each trial, because we don't want tasters learning during the study. Each student records their number of correct identifications on the white board. We aggregate the data for the whole class and use the class data to perform a significance test.
We worked through the STATE part of the process as a whole class. This is mostly to make sure students understand that the null hypothesis is p = 0.20. This is the proportion of correct identifications we would get by simply guessing (remember there are 5 flavors).
FOUR-STEP PROCESS
This is the first time that students will be required to use the four-step process of STATE, PLAN, DO, CONCLUDE for a significance test. 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.
Formalize Later
Here are some tips for using the four-step process for inference:
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Maintain high expectations for what students should be producing. Clearly communicate these expectations and hold them accountable when grading.
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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.
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Don’t reveal calculator commands or applets yet. Of course, all the work of today’s lesson can be done with 1-PropZTest on the TI 83/84 calculator or using the One sample z test for a proportion applet. It is important that students become familiar with the formulas and process for performing a significance test. At the end of the chapter we will reveal the calculator commands for significance tests (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.