1. CAP Statistics Workshop April 1, 2017
Confidence Intervals
Elizabeth Flynn
College of the Canyons

2. Housekeeping... Did everyone...
get a card, write your age (in years) on it, then place your card in the basket? Note: no need to write your name... just your age in years.
get a chocolate candy?

3. ... and one more thing...
Circulate the basket with each of our ages in it
Each person is to give the cards a quick mix and pick out four cards, write down the ages found on each of the four cards on a scratch piece of paper (put this aside; we will come back to this), then put the four cards back into the basket and pass it on to the next person
The basket needs to circulate to everyone
We will return to this data later; I promise 

4. NOW we are ready to get started!
I’m excited!

5. Odd Man Out
Within your table groups, come to a consensus of which of the following (on the next slide) does not ‘go’ with all the others. Be sure you are able to clearly explain your reasoning.
You will have about 5 minutes to discuss, debate, come to a consensus, and formulate an explanation.
Choose a person from your table group to be your spokesperson to report out.

7. Why do you think we did this activity?
You have about 5 minutes to discuss your thoughts regarding this question.
Choose a spokes person from your table group to report out (must be someone other than the person who reported out previously)

8. Big Idea There is no one correct answer or solution
There are several correct approaches, many correct ways to view a situation, to tackle a (statistics) problem, with many entry points... All valid, all correct
Creative entry points are valued and recognized

9. Confidence what’s?
This is what we will explore today... Different, interesting entry points when first exploring the idea of confidence intervals
All with little to no teaching having been done on the actual concept of confidence intervals
The ‘set up’

10. Do we need to do it all???
We will do three confidence interval set-up activities today
Do not feel obligated to do all of these activities in your class
Choose one or two. See how it goes. See how your students receive the concepts. Use a formative assessment to gauge their understanding
You be the judge if they need more introductory activities or not

11. How are we doing with the basket ?

12. Time to change it up; we are moving 
Please group yourselves based on your birth month
All January birthdays sit at one table, all February birthdays sit together at the same table, etc.
Two minutes; go!

13. ... is how old?!?
In your groups, you must come to a consensus for each of the following questions. After your group is in agreement, someone from your group come up to the white boards and mark your group’s response with a tally mark under the appropriate category.
If you happen to know their age or birth date, please recuse yourself. Here we go.

14. ... is how old?!?!
How certain are you that you can guess their age within 25 years of his actual age (plus or minus 25 years)? Your answer choices are:
Certain Likely Somewhat Likely Unlikely No Way!
How certain are you that you can guess their age within 10 years of his actual age (plus or minus 10 years)? Your answer choices are:

15. ... is how old?!?!
How certain are you that you can guess their age within 1 year of his actual age (plus or minus 1 year)? Your answer choices are:
Certain Likely Somewhat likely Unlikely No Way!
How certain are you that you can guess their age within 3 months of his actual age (plus or minus 3 months)? Your answer choices are:

16. ... is how old?!?!
How certain are you that you can guess their age within 1 day of his actual age (plus or minus 1 day)? Your answer choices are:
Certain Likely Somewhat Likely Unlikely No Way!

17. Think-Pair-Share What do you notice about our tally marks?
Why do you think we did this activity?
What’s the big idea? What’s the take-away?

18. Possible Extensions... Once your class has learned about confidence intervals...
Come back to this; take a picture, post on your website
Discuss how (ideally) we want it all. We want to be certain/highly confident AND we want a reasonable range of values (+ or – 25 years is worthless)
For example, I claim that the typical temperature in Santa Clarita is between -200 degrees Fahrenheit and +150 degrees Fahrenheit. Thoughts?
Now I claim that the typical temperature in Santa Clarita is between degrees Fahrenheit and degrees Fahrenheit. Thoughts?

19. Beans!
I’m lazy and don’t want to have to separate all the beans into like groups, then count how many there are in each group
Shake up the bag really well to mix up all the beans; then take a scoop of the beans
Let’s separate the beans and count the number of red beans in the sample and the total number of beans in the sample

20. Beans! In our sample, we have xx/xx or about xx% red beans
Based on our sample, my best guess is that there are between 90% and 95% red beans in the entire bag.
Choose a corner: Totally agree, somewhat agree, somewhat disagree, no way!
As a ‘corner group’ discuss why your choice is correct; share out

21. Beans! In our sample, we have xx/xx or about xx% red beans
REVISED: Based on our sample, my best guess is that there are between 55% and 65% red beans in the entire bag.
Choose a corner: Totally agree, somewhat agree, somewhat disagree, no way! Discuss your choice for two minutes, then share out.
As a ‘corner group’ discuss why the other ‘corner group’ choices are not correct; share out

22. Beans! Return to your table groups
What would happen if we took another sample? Would we get the same sample proportion? Would your ‘corner’ decision change possibly if we took another sample?
Would you like to know the true proportion of red beans in the entire bag?

23. Beans! Possible Extensions?
Within your table groups, come up with one possible extension or follow-up that could tie in this activity to something that students read or hear in the news on a regular basis. Five minutes.

24. Beans! Other Possible Extensions...
Link confidence intervals with hypothesis testing
The possibility of getting an extreme sample (leading into type I and type II errors when conducting a hypothesis test)
I did something tricky with my AP Stats students ...

25. How are we doing with the basket?

26. How old are we, anyway?
Each of you were given a small paper and asked to put your age on it in years; all papers went into the basket
The basket circulated to everyone; each person mixed up the papers, and randomly chose four, and wrote those ages down on a scratch piece of paper, then replaced the papers back into the basket
Now, please calculate the mean age (in years) from the four papers you chose; then plot your mean on the dot plot on the board

27. How old are we, on average?
My claim: The true mean age for all of us is between ____ and ____
You be the judge. Judge my statement as impossible, highly unlikely, unlikely, likely, highly likely, or certain.
Speed date. Everyone up and you will speed date for 1 minute per round, sharing your reasoning why you judged my statement as you did.

28. Let’s Wrap it Up...
These closure ideas are meant to be used once the concept of a confidence interval has been discussed and practiced
Write a meaningful paragraph that includes at least four of the following terms: sample, population, confidence interval, confidence level, estimate, margin of error OR
Write a meaningful paragraph to someone who knows/understands little to not statistics that explains why we calculate/use confidence intervals. Be careful of your vocabulary; use words they will understand. Your paragraph must be four to five sentences.

29. Let’s Wrap it Up... Possible extension...
“My best no” with paragraph at next class session using document camera or other technology
Note: Today, sometimes we were using small sample sizes

30. My goals today...
Promotion of affective domain strategies, low-stakes collaborative practice, thinking-oriented activities, just-in- time remediation
Modeling sound teaching/learning techniques such as think-pair-share, changing groups, speed dating, etc.
Modeling set-up, activity, closure
#1: Jump in with two feet; #2 then explain

31. Thank you!
Elizabeth Flynn College of the Canyons