Multiple testing problem Each student tosses both a penny and a nickel 50 times each, and performs a test of the hypothesis H0 p1 p2 versus H1 p1 p2, where p1 is the probability of heads for the penny and p2 is the probability of heads for the nickel If some students reject H0 at the 0 05 level, can we conclude the probabilities for coins were different Or is there a better explanation Construct a histogram of the P values Is it approximately uniform How does the uniform distribution of the P value explain the relationship between the significance level and the probability of a Type I error

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Question: Multiple testing problem: Each student tosses both a penny and a nickel 50 times each, and performs a test of the hypothesis H0: p1 =

Multiple testing problem: Each student tosses both a penny and a nickel 50 times each, and performs a test of the hypothesis H0: p1 = p2 versus H1: p1 ≠ p2, where p1 is the probability of heads for the penny and p2 is the probability of heads for the nickel. If some students reject H0 at the α = 0.05 level, can we conclude the probabilities for coins were different? Or is there a better explanation? Construct a histogram of the P-values. Is it approximately uniform? How does the uniform distribution of the P-value explain the relationship between the significance level and the probability of a Type I error?

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