Experience First

The previous lesson (Lesson 7.3) was about the sampling distribution of a sample proportion. This lesson and the next are about the sampling distribution for a sample mean. In this lesson, we start with a population distribution that is approximately normal (height of power forwards in the NBA). In the next lesson, we will investigate what happens when the population distribution is not normal (height of shooting guards in the NBA). 

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There is an extra handout that you will need to make copies of or display during the lesson. Also, you will need to prepare a poster for a dotplot (expect values between 77 inches and 84 inches) and students will need sticker dots. 

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Remind students that they will need to stop after question #5. The debrief after question #5 will reveal the formulas for calculating the mean and standard deviation of the sampling distribution, which is needed to complete question #6. 

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Formalize Later

The dotplot provided in the extra handout is the population distribution and each dot represents the height of one power forward in the NBA. The dotplot created in the activity is the sampling distribution and each dot represents one sample of 5 power forwards and the mean height calculated from that sample. Be sure to ask students "What does this dot represent?" for the sampling distribution. 

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Using correct notation in this lesson is critical. For the population distribution, we use mu for the mean and sigma for the standard deviation. For the sampling distribution, we use mu(xbar) for the mean and sigma(xbar) for the standard deviation. 

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If you have a small class and are worried that your dotplots will not have enough dots to reveal shape, you can use this StatKey applet, which allows you to upload the population data and then create sampling distributions with different sample sizes. 

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Be sure to point out the justification for why we know the sampling distribution is approximately normal: because the population distribution is approximately normal. It seems quite reasonable that if we take samples from a normal distribution, that the means of those samples would also follow a normal distribution. But what happens if the population distribution is NOT normal? We will investigate this question in the next lesson when we use the distribution of heights for shooting guards in the NBA (skewed left). 

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In Chapter 9, we will perform a one-sample t test for a mean. The standardized test statistic (which will lead us to the P-value) will be given by the following formula. Can you see how students are actually already doing this calculation as a z-score right now? In Chapter 8 we will discover why to use a t distribution instead of a Normal distribution.