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Estimating a Difference between Two Means

Chapter 9 - Day 5 - Lesson 9.3

Learning Targets
  • Describe the shape, center, and variability of the sampling distribution of a difference between two sample means.

  • Check the Random and Normal/Large Sample conditions for constructing a confidence interval for a difference between two means.

  • Use the four-step process to construct and interpret a confidence interval for the difference between two means.

Activity: Which cookie has the most chips?
Answer Key:

Today we will be investigating which brand of cookie has more chocolate chips.  You will need Chips Ahoy chocolate chip cookies and store brand chocolate chip cookies.  We used Meijer Chipsters so make sure to change the name in the activity if you use something else.  Give each student one of each type of cookie.  They need to count the number of chocolate chips in each cookie.  Students had some questions about how to do this: Should they break the cookie apart? Do they count only the chips they can see? What if it’s not a whole chip?  As long as the students are consistent with each cookie, it doesn’t matter.  When they’re done, they should record the data on the board.

Intro Day 130.jpg

We’ll need to find the sample mean and standard deviation.  You could have students do this in their groups or you could do it for the class to save time.  To find the mean and standard deviation of the sampling distribution, you can tell students the formulas or you can give them a few minutes to discuss what they think they will be.  After going through this, give students about 5 more minutes to calculate the confidence interval and to decide if they have convincing evidence that there is a difference in the average number of chips.

When students have found their interval, make sure to spend time talking about how does a confidence interval give us convincing evidence.  We focus on whether or not the interval contains 0.  Once it’s decided if there is evidence, we need to decide which brand has more.  It’s important talk about how the order of the samples is important.  We added this notation to the margin:

If the interval is:

  • ( + , +) then the first population mean is greater.

  • ( – , – ) then the second population mean is greater.

  • ( – , + ) then we don’t know which is greater so we don’t have convincing evidence.

Turns out, Meijer Chipsters had more chocolate chips than the Chips Ahoy cookies.

Teaching Tip:

We’re not really sure what happened, but there seems to be a very clear food theme second semester.  Perhaps it’s due to the fact that Lindsey was pregnant this semester.  Hopefully you’ve saved your classroom money up because you may be buying a lot of food!  See Days 98, …  It’s gotten to the point that if there is a context involving food and we don’t bring that food in, the students are shocked.  It’s a well known fact that if you want to engage students, just bring in food.  They teach that in the College of Ed right?

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