STAT100B_HW2S

# STAT100B_HW2S - STAT 100B Homework 2 Solutions Denise Tsai...

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STAT 100B: Homework 2 Solutions Denise Tsai January 31, 2011 1. Suppose we flip a coin 100 times independently and we get 55 heads. (a) Test H 0 : p = 1 / 2 vs H 1 : p > 1 / 2, and calculate the p-value. Solution: Z = ˆ p - p 0 q p 0 (1 - p 0 ) n = 55 100 - 0 . 5 0 . 5(1 - 0 . 5) 100 = 1 The p-value: P ( Z > 1) = 1 - P ( Z 1) = 1 = 0 . 8413 = 0 . 1587 We do not reject the null hypothesis. Therefore, there is strong evidence to claim that the coin is fair. (b) Suppose the decision rule is to reject H 0 if ˆ p > . 6. What is the probability of type I error? If the true value of
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