The New Scientist (January 4, 2002) reported on a controversy surrounding the Euro coins that have been introduced as a common currency across Europe. Each country mints its own coins, but these coins are accepted in any of the countries that have adopted the Euro as their currency.

A group in Poland claims that the Belgium-minted Euro does not have an equal chance of landing heads or tails. This claim was based on 250 tosses of the Belgiumminted Euro, of which 140 (56%) came up heads. Should this be cause for alarm for European sports fans, who know that “important” decisions are made by the flip of a coin? In this activity, we will investigate whether this should be cause for alarm by examining whether observing 140 heads out of 250 tosses is an unusual outcome if the coin is fair.

1. For this first step, you can either (a) flip a U.S. penny 250 times, keeping a tally of the number of heads and tails observed (this won’t take as long as you think), or (b) simulate 250 coin tosses by using your calculator or a statistics software package to generate random numbers (if you choose this option, give a brief description of how you carried out the simulation).

2. For your sequence of 250 tosses, calculate the proportion of heads observed.

3. Form a data set that consists of the values for proportion of heads observed in 250 tosses of a fair coin for the entire class. Summarize this data set by constructing a graphical display.

4. Working with a partner, write a paragraph explaining why European sports fans should or should not be worried by the results of the Polish experiment. Your explanation should be based on the observed proportion of heads from the Polish experiment and the graphical display constructed in Step 3.