You’ve made it to Unit 7! Where we get to go over confidence intervals and significance tests all over again, but with problems involving means. The Central Limit Theorem makes a comeback in this unit, and students are introduced to the t-distribution; a beautiful solution to not knowing the population standard deviation in the majority of inference procedures. The AP exam is looming closer, and we can start to see the finish line. Let’s get into the setup of this unit!
In this unit, I start off with an activity called “Walk It Out”. I got the idea for this activity years ago from another teacher and it has evolved into what I now run in my class.
Intro Activity
It takes a bit of setup before class. I use painter’s tape to mark up 100ft on the floor in the hallway. If you are not able to use the hallway for this activity, you can mark a straight line of painter’s tape as far as you can go in your classroom, and then if a student reaches the end before they step off the line, you can leave them back to the front to continue their walking.
There are four questions that you and the students will answer together before you start the activity, talking about what you will be able to expect. One of the questions asks students to define what “walking off the line” will look like. Most students say that the first full step off of the line will stop their progress and we will measure from the tip of their foot that is still on the line. You can be flexible on what is “on the line” and “off the line” and where you will measure the distance from, but just be sure to define that beforehand. We also had to have a rule where students needed to walk one foot at a time down the line. No running, skipping or hopping. I ask if there is a rule that says students need to walk forwards, or if they can side-step. Again, I’m flexible on rules with them, but we just make sure to define all of this beforehand.
We gather everyone’s data (if you have a small class, you can ask them to go twice), and that is usually all we have time for in a 50-minute class period. The next day, we go through a data analysis, where students use 3 different ways to check if their class data follows a normal distribution. Usually, it does, but I have had a few classes where it didn’t! We always still do the inference questions, but when we get to our conclusion for this activity, we say that our results probably can’t be trusted because it doesn’t fit the normal model. The data analysis takes up at least 30 minutes (sometimes a little more if you have a chatty group), so I wait to start Notes 1 until the next day.
If you feel pressed for time, and do not want to use two full class periods for this activity, feel free to start right away with Notes 1 in this unit. Students will learn right away about creating a confidence interval for a mean with a known standard deviation since they have learned about confidence intervals in Unit 6. We talk about how we do not know the population standard deviation however, and if we use the sample standard deviation instead, that will introduce even more error into our confidence interval, so to accommodate for that, we have the t distribution.
My Pacing:
Day 1: Walk It Out Activity, Gather Data
Day 2: Walk It Out Activity, Analyze Data
Day 3: Notes 1 – Confidence Intervals for Means
- One Sample Z-Interval
- t Distributions
- One Sample T-Interval
Day 4: Notes 2 – Significance Tests for Means
- One Sample Z-Test
- One Sample T-Test
- Interpreting Errors
Day 5: M&M Activity: Testing a Claimed Mean
Day 6: Unit 7 Quiz
Day 7: Notes 3 – Margin of Error and Matched Pairs
- Margin of Error for Means
- Matched Pairs Data
Day 8: Notes 4 – Difference Between Two Means
- Sampling Distribution of a Difference in Means
- Two-Sample Z Statistic
- Two-Sample T Statistic
- Two-Sample T Interval for Means
- Two-Sample T Test for Means
- Practice Problems
Day 9: Finish Notes 4
Day 10: Notes 5 – Choosing Your Inference Method
- Comparing Inference Methods
- Summarizing CI and HT for Means
- Recapping CI and HT for Proportions
Day 11: Work Day
- Unit 7 Summary Slides
- Unit 7 Test Review
- Project: Hypothesis Testing
Day 12: Unit 7 Test
For Unit 7, the AP Statistics CED recommends 14 to 16 class periods. I usually take about 12 to get through the notes and assignments. I am always feeling the time crunch for the AP exam right about now, so if my students are doing good, I like to move right into Chi-Square tests as soon as I can after this unit.
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