Y is a bernoulli random variable with probability pr

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Y is a Bernoulli random variable with probability Pr ( 1) Y p = = and Pr ( 0) 1 . Y p = = From the solution to Exercise 3.2, Y has mean p and variance (1 ). p p (a) . (b) ˆ ˆ (1 ) 0.5375 (1 0.5375) 4 400 ˆ var( ) 6 2148 10 . p p n p × = = = . × The standard error is . (c) The computed t -statistic is Because of the large sample size ( 400), n = we can use Equation (3.14) in the text to get the p -value for the test 0 0 5 H p : = . vs. 1 0 5: H p : . -value 2 ( | |) 2 ( 1 506) 2 0 066 0 132 act p t = Φ − = Φ − . = × . = . (d) Using Equation (3.17) in the text, the p -value for the test 0 0 5 H p : = . vs. 1 0 5 H p : > . is
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