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Mini-Project: Cents and the Central Limit Theorem
1. Collect a sample of at least 50 pennies by setting aside all the pennies you receive in change for several days. Do NOT use pennies from your penny jar – you want pennies that are in circulation now. For each of your pennies, record its age (subtract its date from the current year).
2. Use your data to construct a histogram of the ages of your pennies. Describe its shape. Are there any outliers? Report the mean and standard deviation for the ages of your collection of pennies. YOU DO NOT HAVE TO INCLUDE YOUR ACTUAL HISTOGRAM.
3. Take 20 random samples of size 5 from your collection of pennies (yes, with replacement); for each sample, compute its mean.
4. Use your sample means to construct a histogram using the same scale as your histogram from part 2. Describe the shape of this new histogram. Are there any outliers? Why does your histogram have this shape? Report the mean and standard deviation for your set of sample means. Compare these numbers to the numbers from part 2. What do you observe? YOU DO NOT HAVE TO INCLUDE YOUR ACTUAL HISTOGRAM.
5. The histogram you made in part 4 is a picture of the sampling distribution of the sample mean for samples of size 5 (chosen randomly from the population of pennies like yours). Without actually taking any more samples, describe the sampling distribution of the sample mean for samples of size 25 and say what the mean and standard deviation would be.
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