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Fairness of U.S. Quarters, Nickels, and Pennies

Fairness of U.S. Quarters, Nickels, and Pennies. By: Nate Golomb. 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.

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Fairness of U.S. Quarters, Nickels, and Pennies

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  1. Fairness of U.S. Quarters, Nickels, and Pennies By: Nate Golomb

  2. 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.

  3. 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.

  4. Experiment • The 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%.

  5. Spinning Coin Demonstration

  6. Quarter Results • Proportions – Heads: 77/150; Tails: 73/150 • Percentages – Heads: 51.33%; Tails: 48.67%

  7. Nickel Results • Proportions – Heads: 64/150; Tails: 86/150 • Percentages – Heads: 42.67%; Tails: 57.33%

  8. Penny Results • Proportions – Heads: 51/150; Tails: 99/150 • Percentages – Heads: 34%; Tails: 66%

  9. Quarter 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.

  10. Nickel 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.

  11. Penny 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.

  12. Overall 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.

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