How can you tell if a given coin is biased?

Determining if a coin is biased involves testing whether the coin lands on heads or tails with equal probability. Here's a step-by-step approach to figure out if a coin is biased:

1. Formulate a Hypothesis

• Null Hypothesis (H0): The coin is fair (i.e., the probability of landing heads is 0.5).

• Alternative Hypothesis (H1): The coin is biased (i.e., the probability of landing heads is not 0.5).

2. Conduct a Series of Trials

• Flip the coin a large number of times (e.g., 100, 200, or more). The more trials, the more reliable your results.

• Record the outcome of each flip (heads or tails).

3. Calculate the Proportion of Heads

• Count the number of heads HH and the total number of flips NN.

• Calculate the proportion of heads: p=Number of Heads / Total number of flips

4.Calculate the Z-Score:

• The Z-score measures how many standard deviations the observed proportion is from the expected proportion.

compate the z score aginst the established confidence level established and pvalue to determine if we can reject the null hypothosis or not