Every year in AP stats for the last 4 years I have struggled with getting my learners to understand and use the all important conditions checks in Confidence Intervals and Hypothesis tests. This year I changed up how I taught it, and it has really made an impact. In fact, I can honestly say that all of my learners are using and completing the conditions checks with consistency.
Here is what I did.
First, there are two essential assumptions / conditions:
1. Randomization – is the data collected through some sort of random process (usually given)
2. Independence – what makes the data independent? Stop and think about the context.
Okay, those two generally are not the problem, because they are the same across all types. No mess, no fuss, stop, think and read and think again and you have those two. It is the next two that requires the real thought and memorization. I changed it up this year and put my own spin on them. Instead of naming them as the book, I realized that what they are trying to set is the maximum and minimum sample size that will give you an appropriate sample:
|Z CI or HT||T CI or HT|
|3. Max Sample Size||n < 10% of population of interest||n < 10% of population of interest|
|4. Min Sample Size||np & nq >= 10||3 parts to “nearly normal”|
With this kind of setup, they are thinking about the context more. Why do they have to check the 10% condition? Because that gives you a ceiling on your sample size. Why the success / fail condition? It gives you the floor to the sample size.
My learners are much more focused and they are planning better this year on this topic. I am very pleased by how fluid and easily they are incorporating the CI’s and the HT’s into their language, whereas in prior years it was a struggle to get them to memorize what they were doing.
I think the fact they understand why is making a difference.