Math 113A&B: LAB #2                                                                                                       Due: Fri. 3/29/02

R. Lock  3/25/02                                                                                                                                    10 pts



            Are pennies really fair?  Let’s determine the effectiveness of several methods for “flipping” a penny to see if the proportion of heads is really one half.  You may work alone or choose one other classmate to work with and submit a common report to address the four items outlined below.  Here are the methods you will investigate.  In each case, we will be interested in the proportion of heads produced.


A.       Penny Flipping - Toss the penny into the air, letting it flip over and over, then catch it.


B.       Penny Spinning - Hold the penny on its edge on a smooth flat surface - a dining hall table might work well.  Flick one side to cause it to spin rapidly.  Wait until it settles down to see which side ends up facing up.  Note: Don’t count spins that fail to rotate well, hit something before coming to rest, or fall off the surface.


C.       Penny Tipping - This requires a bit of skill and patience.  Get a penny to rest on its edge on a smooth level surface, then jar the surface (e.g. bang it - but gently!) until the penny falls over.  You might want to try getting several pennies to balance at once before hitting the surface, but don’t count instances where a penny is prematurely knocked over by physical contact.


Note:  When generating a sample, you may use a single penny repeatedly or several different pennies.  You may also enlist the aid of friends in producing your samples.


Here’s what you need to report on:


1.     Estimate the proportion of heads by flipping a penny one hundred times.  Use your estimate to compute a 90% confidence interval for the true proportion of heads.


2.     How large a sample would you need to estimate the proportion of heads to within 0.10 with 90% confidence?


3.     Use the sample size from #2 (or one slightly larger) to find a 90% confidence interval for the proportion of heads obtained by spinning a penny.   Can you conclude from your CI result alone that the proportion is significantly different (at a 10% level) from p=0.50?  Explain


4.     Obtain a sample of at least n=50 penny tippings.  Estimate the proportion of heads and test whether it is significantly different from 0.50.  Choose your own significance level and include the calculation and interpretation of a P-value.



Bonus:  Provide documented evidence (for example, a photo) that you satisfied part #4 by getting 50 pennies to stand simultaneously before tipping them to earn an extra point.