**Extra Credit Hand-in
Assignment: up to 20 points added to your HW total**

**Due Wednesday, December 14
(this is the reading day – drop it off in my mailbox in SB 308) **

**Late submissions are not
accepted (however, early submissions are encouraged!)**

**Multiple pages must be
stapled or it will not be accepted.**

** **

Please complete these problems on a separate page,
and please type all explanations and interpretations. You must show all work and ** work
individually** on these problems.

For
some perverse reason, I am interested in estimating the mean year stamped on
pennies currently in circulation. It is
known that the population of years on all pennies in circulation is skewed to
the left (i.e. definitely **not** normal.)

a.
Why
does it make sense that this population would be skewed to the left?

b.
I
read somewhere that the mean year on pennies in circulation is currently
1986. I would like you to test this
statement against the alternative claim that the mean year is actually later
than 1986 at the 0.01 level of significance.
State the hypotheses and the rejection region for this test. What assumptions and/or facts that we have
studied are you using?

c.
Since
the population is skewed, any estimate of the mean that we do should be based
on a large sample. The sample should be
representative of the population of pennies currently in circulation (i.e.
shouldn’t consist of old pennies in a collector’s book, for instance) and ideally
should be random. Briefly describe a way
that you could obtain a sample of fifty pennies in circulation that fits these
requirements.

d.
Following
the method you outlined in part c, obtain a random sample of fifty pennies and
record the year stamped on each one.
List your data and hand it in with your assignment.

e.
Using
the data found in part d, carry out the hypothesis test. What is your interpretation of the
results? What is your conclusion?

f.
What
is the p-value for this test? Give an
interpretation of this number. For what
values of alpha would the results of your test be significant?