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Sampling Distribution of a Difference between Two Proportions (Topic 5.6)

Chapter 7 - Day 5

Learning Targets
  • Calculate the mean and standard deviation of the sampling distribution of a difference between sample proportions.

  • If appropriate, use a Normal distribution to calculate probabilities involving a difference between two proportions.

Activity: Do Skittles or M&Ms have more orange candies?
Answer Key:
Teaching Tip

If students didn't think we were serious about applying our statistical knowledge to Skittles before, they get another day to see how we can further our Skittles education. While yesterday had them working with an applet, today we are actually going to let them do some counting of physical candies. We have a bag that we reuse every year, but if you are feeling generous you could also bring in some mini bags for added fun. Check out EFFL on a Budget, for thoughts about other ways to approach activities like this. 

We find it best to let the students start working through page 1, and then coming back to the class to debrief page 1. A lot of students will do great at ball parking the center, but struggle a little more on the standard deviation. If they have found the distribution to be approximately normal, guide them to the empirical rule to allow them to come up with an approximation.

At this point, we don't need to worry too much about the correct values. They will learn how to get the exact values on the second page of the activity. When they work on the second page, remind them that the boxes will all be review from yesterday, but question 6 & 7 will have them combining skills from the past. In problem 7, we underline with the student that they are finding the probability of the difference in proportions to help them come up with the correct normal distribution. 

Teaching Tip

Make sure to throw this lesson back to combining random variables in Unit 4. Students will need to remember:

Luke's Lesson Notes

Here is a brief video highlighting some key information to help you prepare to teach this lesson.

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