Are U.S. Coins Fair?Are U.S. Coins Fair?

Coins are used to decide disagreements with a flip or spin, to determine the start of a sporting event, coin games involving spinning/flipping, etc.

Are we sure all coins are fair and acceptable for these ordeals?

To test the question, spinning a coin on a flat surface will be used because an unfair weighting has less an affect when flipped versus when the coin is grounded.

Rumor has it…Rumor has it…

Quarters are said to be fairly weighted; the ratio of heads/tails should be 50%.

Thus, if fairly weighted, heads will come up the same number of times as tails.

Nickels and Pennies are rumored to have more weight on the head’s side causing tails to come up more often when spun on a flat surface.

ExperimentExperimentThe experiment run used five quarters, nickels, and pennies of all different years to represent a simple random sample of all respective coins in circulation.

Each coin was spun 30 times on a flat surface for a total of 150 possible outcomes.

The number of head and tail outcomes were recorded and proportion significance tests were conducted against the expected ratio of 50%.

Spinning Coin DemonstrationSpinning Coin Demonstration

Quarter ResultsQuarter Results

Proportions – Heads: 77/150; Tails: 73/150

Percentages – Heads: 51.33%; Tails: 48.67%

48.7%51.3%

Category12

Quarters Spun: Heads (1) / Tails (2)

Nickel ResultsNickel Results

57.3%

42.7%

Category12

Nickels Spun: Heads (1) / Tails (2)

Proportions – Heads: 64/150; Tails: 86/150

Percentages – Heads: 42.67%; Tails: 57.33%

Penny ResultsPenny Results

66.0%

34.0%

Category12

Pennies Spun: Heads (1) / Tails (2)

Proportions – Heads: 51/150; Tails: 99/150

Percentages – Heads: 34%; Tails: 66%

Quarter Significance TestQuarter Significance Test

Null Hypothesis: p = 0.5; Alternative Hypothesis: p < 0.5

Test Statistic: z = 0.33

P-Value: p = 0.628

Conclusion: We cannot conclude that the quarter is unfairly weighted causing one side of the coin to come up more than the other when spinning it on a flat surface.

Nickel Significance TestNickel Significance Test

Null Hypothesis: p = 0.5; Alternative Hypothesis: p < 0.5

Test Statistic: z = -1.80

P-Value: p = 0.036

Conclusion: We can conclude that the nickel is unfairly weighted on the heads side causing tails to come up more often when spinning it on a flat surface.

Penny Significance TestPenny Significance Test

Null Hypothesis: p = 0.5; Alternative Hypothesis: p < 0.5

Test Statistic: z = -3.92

P-Value: p = 4.44298 x 10^-5

Conclusion: We can conclude that the penny is unfairly weighted on the heads side causing tails to come up more often when spinning it on a flat surface.

Overall ConclusionsOverall Conclusions

Both pennies and nickels are deemed to be unfairly weighted and unable to provide a fair 50-50 trial or game.

The heavier heads side of the coin causes tails to come up more often when spun on a flat surface.

Dimes were not tested because they have not been rumored as unfair, however, they should be tested before assuming they are fair.

Thus, Quarters will provide a tested, reliable, and fair 50-50 trial or game.