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Math 171 Project: THE AGE OF A COIN – Fall 2015
Have you ever wondered how long coins stay in circulation? Are you a collector? In this project you will
explore descriptive and inferential statistics for the age of pennies and the age of quarters in circulation.
Collect fifty quarters and fifty pennies and record the date that each was minted. Also record whether or not
each quarter that you collect has an eagle on its “tails” side (note that quarters minted before 1999 had eagles,
whereas those minted afterwards are part of special U.S. Mint programs). We are interested in the age of the
coin so determine the AGE of each coin, in years.
Part I: For each type of coin answer the following questions in paragraph form. This should be a
narrative which addresses the bullet points below.
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How did you collect the coins? Do you think your data collection method could possibly introduce bias
into your results? Why /why not?
Describe the population, individuals, variables, and variable types involved in this project.
Represent the distribution of the coin ages using an appropriate graphical summary. Your graphical
summary should be detailed enough to show interesting features of the distribution but not so detailed as
to lose any interesting features.
Find the mean, standard deviation and five-number summary of the ages of the coins in your sample.
Put this information in a single table for easy reading and comparison.
Describe the distribution (shape, center, and spread) of the coin ages. Does the distribution have any
outliers? Why do you think the distribution has the shape you have observed? Discuss any major
differences and/or similarities of the distributions of the ages for each coin type. Explain whether
you think that there is a difference in the mean ages of the coins from your graphical and
numerical summaries.
What about the distribution of all coins in circulation? Do you think that distribution is similar to the
distribution of your samples? Explain your reasoning.
Compute a 95% confidence interval for the mean age of all coins of each type. What is the margin of
error for each of your estimates? Present this data in one table.
Part II: Then we continue the project. Answer each question for the requested type of coin(s).
This part is NOT in narrative form. Number and write each question. Show your reasoning and
work for each question. Your answers should be clearly designated.
1. If you wanted to estimate the average age of pennies to within one year with 99% confidence, then how
large of a sample size would you need to obtain? Use the standard deviation from your sample as your
best estimate of the population standard deviation.
2. Suppose you want to estimate the proportion of pennies in circulation that are older than 20 years to
within 2% with 98% confidence. Use your sample as a pilot study to determine the sample size
necessary to achieve your goal.
3. Is the mean age of all quarters in circulation the same as the mean age of all pennies in circulation? You
will need to use an appropriate inferential technique to the answer this question. Make sure that you
show (and explain) all work that supports your conclusion. You should also produce a nice graphical
representation of the distributions of the ages of your two coin types that makes it easy to compare the
two distributions visually as well as discuss the assumptions necessary to run this inference test in your
particular situation.
4. Working under the assumption that coins stay in circulation for thirty years and examining coin
production figures from the last thirty years, I hypothesize that the proportion of quarters without an
eagle on the “tails” side is 0.62. Use your data to address the validity of my hypothesis using an
appropriate inferential technique.
Math 171 Project: THE AGE OF A COIN
Grading Rubric
You may work in groups of three or fewer students for this project. Only one submission per group is
necessary, but make sure to include a cover page listing everyone in your group who contributed to the project.
This should be pledged. Choose your group mates wisely.
DATES:
Tuesday, Nov. 24
deadline to email list of coin ages and # of quarters with eagles
DO NOT ATTACH—just paste list into e-mail
NOTE – Send AGES, not dates
If you are working in a group, nclude all names in subject line.
Tuesday, Dec. 1
project due at beginning of class
Your project will be graded according to the following rubric:
Feature
Cover Page
Email list of coin ages/eagles to me.
NO ATTACHMENTS PLEASE
Correct use of English.
Organization and Coherence.
Correct description and use of
statistics.
Accuracy and Quality of
Graphs and Tables
Explanation
Title, Name(s), Pledge if group
Include one long column with coin type, then ages,
for each coin type.
You should use complete English sentences with
proper spelling, grammar, and punctuation.
PART I
Your work should be clearly organized so that I can
easily follow all statements and find any graphs or
tables. Your narrative should flow nicely. Keep coins
together in the narrative; do not separate into a penny
narrative and a quarter narrative.
Points
1
2
10
15
Self explanatory
15
Use SPSS for graphs.
Tables should be clearly labeled.
21
PART II
Question 1
Question 2
Question 3
Question 4
7
7
13
9
Total
100
2