Testing a Claim about a Difference Between Two Means (Lesson 10.4)
Chapter 10 - Day 5
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
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Learning Targets
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State hypotheses and check conditions for performing a significance test about a difference between two means.
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Calculate the standardized test statistic and P-value for a significance test about a difference between two means.
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Use the four-step process to perform a significance test about a difference between two means.
Experience First
In the state of Michigan, there is no bigger rivalry than Michigan versus Michigan State (GO BLUE!). You may want to edit the Word document to include colleges from your region.
Students might need some support in coming up with the hypotheses for this significance test. We suggest starting with the alternative hypothesis and looking at the wording of the question:
Do these data provide convincing evidence of a difference in the mean number of points per game for the two teams?
Students should be able to turn this into the alternative hypothesis: mu1 /= mu2. Help them to see that this is exactly the same as writing mu1 - mu2 /= 0. Then from last chapter, we know that the null hypothesis always says the parameter is equal to some value, so we get a null hypothesis of mu1 - mu2 = 0 (or mu1 = mu2).
Students will use the Two sample t test for means applet (part of the Traditional Inference applets at www.statsmedic.com/applets. Be sure students use the Input dropdown set to "Mean and standard deviation" and the Conservative degrees of freedom set 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 is perfectly acceptable to subtract in the other order (MSU - Michigan), as long as you are consistent with this choice throughout. The correct t-test statistic would be t = -1.036 and the P-value would be the same.
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The Random and Normal/Large Sample conditions need to be checked for two samples (twice the work!).
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Don't forget about the interpretation of the P-value (after all it is the holy grail). Students don't need to write this down, but it will help them to better understand the conclusion:"Assuming the null hypothesis is true (the mean number of points is the same at Michigan and MSU), there is a 0.306 probability of getting a difference of sample means of 2.3 or greater purely by chance."
Because we skipped the calculation and allowed students to use the applet to get the t test statistic and P-value, 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.