Significance Test for a Proportion
Day 94 - Lesson 9.2
Perform a significance test about a population proportion.
Activity: Can You Taste the Rainbow?
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. Help students to 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).
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.
The Four-Step Process
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 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/Normal Condition: so the sampling distribution of the sample proportions will be approximately Normal and we can use z to find a P-value.
Don’t reveal calculator commands yet. Of course, all the work of today’s lesson can be done with 1-PropZTest on the TI 83/84 calculator. It is important that students become very 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. 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).
4-Step White Board Critique
We used the Check Your Understanding to do a White Board Critique. Here is how it works:
Assign students a 4-step problem to work on in pairs.
Monitor the room to support student learning. As each pair finishes, send them to the white board to write up 1 of the steps STATE, PLAN, DO, or CONCLUDE. The first two pairs should handle the PLAN and the DO because they take the longest to write up.
Once all 4 steps are on the board, call the class back together as a group. Ask them to critique the solution on the board as if it were a quiz or test question. Make any revisions with a red marker. This is your opportunity to make clear your expectations for a 4-step problem on an assessment.