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

R. Lock 3/25/02 10 pts

**PENNY
PROPORTIONS**

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.

===========================================================================