Estimating a Difference Between Two Means (Lesson 10.3)
Chapter 10 - Day 4
Chapter 10
Day 1
Day 2
Day 3
Day 4
Day 5
Day 6
Day 7
Day 8
Day 9
Day 10
Day 11
Day 12
Day 13
Day 14
All Chapters
Learning Targets
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Check the Random and Normal/Large Sample conditions for constructing a confidence interval for a difference between two means.
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Calculate a C% confidence interval for a difference between two means.
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Use the four-step process to construct and interpret a confidence interval for the difference between two means.
Experience First
Cookie day! You will need to buy a box of Chips Ahoy and a box of the generic brand chocolate chip cookies (for us here in Michigan it is the Meijer Chipsters). Students will work in pairs to break apart one cookie from each brand to estimate how many chocolate chips per cookie. Yes, they can eat the cookie once the data are collected!
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As is now the theme in this chapter, we are allowing students to use an applet to calculate the confidence interval, rather than using formulas. This will again allow us to focus more energy on interpreting the confidence interval.
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Students will use the Two sample t interval for means applet (part of the Traditional Inference applets at www.statsmedic.com/applets). Students can use this applet at the very beginning of the activity to find sample statistics, and also the end of the activity to calculate a confidence interval. When calculating a confidence interval, students should leave the "Conservative degrees of freedom" to "No".
Formalize Later
When debriefing the activity, here are a few items to highlight:
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When defining the parameter, it is important to include the word "difference" and to clearly indicate the order of subtraction.
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It would have been perfectly acceptable to subtract in the other order (Generic - Chips Ahoy), as long as you are consistent with this choice throughout. The correct interval here would be (-6.07, -1.469).
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The Random and Normal/Large Sample condition now need to be checked for two samples (twice the work!).
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Remember that a confidence interval gives a list of plausible values for the parameter. In this activity, it is plausible that Chips Ahoy has from 1.469 to 6.07 more chocolate chips than the generic brand, on average.
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If the confidence interval contains 0, it is plausible that there is no difference in the mean number of chocolate chips for Chips Ahoy and the generic brand.
Because we skipped the calculation and allowed students to use the applet to get the confidence interval, the discussion about degrees of freedom is not needed. For those interested, there are two approaches:
1. The conservative approach. Use the smaller of the two degrees of freedom from the two samples.
2. Use a fancy formula to calculate the degrees of freedom. This is what the applet is using to get the df.
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