You have a coin and you would like to check whether it is fair or biased. More specifically, let θ be the probability of heads, θ = P(H). Suppose that you need to choose between the following hypotheses:

We toss the coin 100 times and observe 60 heads.

1. Can we reject H₀ at significance level α = 0.05?

2. Can we reject H₀ at significance level α = 0.01?

3. What is the P-value?

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Ho (the null hypothesis): The coin is fair, i.e., 0 = 0o = 1/ H₁ (the alternative hypothesis): The coin is not fair, i.e., 0 > 2.