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. You may not receive help from tutors or others.
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?