How would one obtain a random sample of pennies (from the U.S)? I am doing a project for my Statistics class to answer the question: "Is there a relationship between the year and the number of pennies minted that year?". I need a random sample of pennies, but don't know where to start. I do have a container at my house full of pennies, and I was thinking I could use that, or maybe I can go to a bank to obtain them. Any suggestions?
 A: In a random sample, every member of the population has an equal chance of being selected, and the selection of one member of the population does not alter the probability of any other member being selected.
You're going to have problems getting a random sample. How long have you been collecting pennies in your jar? If it's a long time, then newer pennies will be under-represented. 
Do newer pennies start their journey in a particular place, and then move out from there? If you're near that place, the pennies will be newer than the population. If you're far from it, you'll have fewer new pennies.
According to this page: https://www.coinstudy.com/old-us-penny-values.html Some pennies from particular years are very valuable (up to $600). You're not likely to find many of those.
But (IMHO) none of this matters. You're doing this for your own education. You don't need to find out the answer, you need to learn from this. Finding a good sample of pennies will waste time that you could be using to understand the problem.
Use the jar of pennies in your house, think of the reasons this might be unrepresentative (I thought for a couple of minutes) and include that in your discussion in a section on shortcomings. That shows you can analyze data and think about the limitations of your analysis. 
A: There are many sources online where you can look up exactly how many pennies were minted per year at each of the three US mints. (The two most obvious are Wikipedia and the US Mint's own website.). 
The best you can hope to accomplish by collecting pennies from various sources is to speculate on how the distribution of pennies in each sample differs from a theoretically random distribution. You will not be able to prove anything meaningful without collecting thousands, perhaps tens of thousands,  of pennies. 
Some sample questions: 
(1) what factors other than distance from the mint affect the relative proportion of pennies minted in Philadelphia, Denver, and San Francisco collected at different locations?  
(2) Are there statistically meaningful differences in pennies collected from personal penny jars and small penny candy vending machines? Pennies bought in rolls from banks? Penny jars from retirees versus children's piggy banks versus working adults?  Poorer versus wealthier neighborhoods? 
(3) are there statistically meaningful variations from place to place in the rate at which minted coins are lost from circulation?  
(4) if you can gather historical comparison data, did the Lincoln Memorial cents (discontinued after 2008) disappear from circulation faster or slower than the Wheat Back pennies (last year 1958)? Was there any noticeable blip from when the penny was converted to lighter cheaper metals? 
Is this a class assignment as given, or did you come up with the idea on your own?  If the former, it may be a good idea to clarify just what your instructor is trying to accomplish with this exercise. 
