Lesson 8.2 – Significance Tests and Decision Making

  • Determine if the results of a study are statistically significant and make an appropriate conclusion using a significance level.
  • Interpret a Type I error and a Type II error in context.  
  • Give a consequence of a Type I error and a Type II error in a given setting.  

 

Activity: Should Flint switch to bottled water?

Type I and Type II error can be really challenging for students.  One of the best ways to get them to understand it is to use contexts that they are familiar with that are easy to grasp.  We started today by talking about the legal system.  In the US, a defendant is assumed innocent (null hypothesis) until proven guilty (alternative hypothesis).  So when does the legal system fail? There are two well publicized cases of this that many students may be familiar with 1) Steven Avery and 2) O.J. Simpson.  Steven Avery is the subject of the Netflix series Making a Murderer.  He was arrested and jailed for 18 years for a crime he didn’t do. This is a Type I error.  The null hypothesis was true but an error was made.  O.J. Simpson is a famous athlete accused of murdering his wife but he was not convicted.  It is widely believed that he did commit the murder, now more than ever after the miniseries O.J.: Made in America aired in 2016.  This is a Type II error.  The alternative hypothesis was true but an error was made.  Give students a few minutes in their groups to discuss which error is worse in this case.

Once students are introduced to the types of error, they are ready for the activity.  We live in Michigan so the Flint water crisis is something our students were very aware of and concerned about.  Feel free to change the context to something your students are more familiar with if necessary.  You could also show a news clip about the water crisis to start the lesson.  The activity is fairly straightforward, and students should be able to work through the entire thing without teacher input.

Notes

Our second year teaching Intro Stats we actually taught this lesson after lesson 8.6, and it went very well.  Students understand a significance test much better so making an error made a lot more sense.  We taught lessons 8.1, 8.3 and 8.4 together and then 8.5, 8.6 and back to 8.2.

 

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