Note: This project was originally designed to study the ages of pennies circulated in the market. Due to the Covid-19 pandemic, it will be difficult to shop in the market in order to collect 50 pennies. As substitute, you may also use nickels, dimes, quarters, and even paper bills.

Project: The Age of a Penny

Have you ever wondered how long coins stay in circulation? Are you a collector?

In this project you are going to collect at least 50 pennies currently in circulation (n 50), and record the ages of the pennies. For example, a penny made in 2021 has an age of 0, 2020 has an age of 1, etc. Your first task is to form a distribution of their ages.

1) List your data. The data should be the age of the penny, not the year it was made.

2) Organize the data by constructing a frequency table with 5 classes.

3) Construct a pie chart.

4) Construct a histogram based on the frequency table.

5) What is the shape of the distribution? Why do you think it is this shape?

6) Did you find any outliers? List the fences.

7) Do you think the distribution of all pennies in circulation is similar to your sample?

8) List the 5-number summary and construct the box plot.

9) Find the mean and standard deviation of the ages of the pennies in your sample.

10) Compute a 95% confidence interval for the mean ages of pennies.

11) What is the margin of error for your estimate?

12) The president of "Coins Unlimited" has just hired you as his chief statistician for his research on the age of pennies. You are charged with the task of estimating the average age of pennies in circulation within one year of age with 99% confidence. How large of a sample would you need to obtain? Use the standard deviation from your sample as your best estimate of the population standard deviation.

13) On the basis of your research with this project, how would you define the age of a "rare" coin? Give a statistical definition for your choice.