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Topic: Pennies for Your Thoughts

In many of the problems from last unit, you were given information about the population. For many of the variables, you assumed the variable had a normal distribution. What if the variables you are studying are not normally distributed? Here is your challenge – if the population is not normal, can you make any inferences about that population from your random samples?

As a class last unit, you have created a population of the ages of pennies. Your instructor will share this Penny Population document with you as an Excel file, that will include the histogram, mean, and standard deviation of this population of penny ages. Your instructor will also share a link to the Sampling Form to be used in step 5. See Example and DB starter video in Unit 5 LiveBinder.

Main Post:

1) Describe the distribution __shape of the population__ of penny ages (i.e., left skewed, symmetric, right skewed).

2) On your copy of the Penny Population document, randomly select 5 penny ages from this population. Calculate the mean of this Nickel Sample (sample size n = 5). How does this compare to the population mean?

3) On your copy of the Penny Population document, randomly select 10 penny ages from this population. Calculate the mean of this Dime Sample (sample size n = 10). How does this compare to the population mean?

4) On your copy of the Penny Population document, randomly select 25 penny ages from this population. Calculate the mean of this Quarter Sample (sample size n = 25). How does this compare to the population mean?

5) Enter your Nickel Sample mean, Dime Sample mean, and Quarter Sample mean in the Sampling Form sent by your instructor. It will generate a histogram of the class means for each sample (Nickel Samples, Dime Samples, and Quarter Samples).

6) Copy and paste the class histograms as they look so far for others to review in the discussion.

Peer Reply #1: Review a classmate’s post. Respond to them as a friend. In a few sentences, explain to them what the Central Limit Theorem says referencing the mean for their Nickel Sample, Dime Sample, and Quarter Sample. See Example.

Peer Reply #2: Review another classmates’ post. Respond to them as a friend. What do you notice about the shape of the histograms for the Nickel samples, Dime samples, and Quarter samples. Do any of their histograms look normal? What can you infer about a Half Dollar Sample (sample size n = 50)? See Example.

Activity based on R.L. Schaeffer et al., *Activity-Based Statistics*