econ310_f09_ps7_ans - Econ 310: Problem Set #7 Solutions...

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Unformatted text preview: Econ 310: Problem Set #7 Solutions Andres Aradillas-Lopez 1. Exercise 5.8 (a) P ( X ≥ 3) = ( 4 3 ) . 52 3 . 48 + ( 4 4 ) . 52 4 . = 0 . 3431. (b) If the coin were fair, P ( X ≥ 3) = ( 4 3 ) . 5 3 . 5 + ( 4 4 ) . 5 4 = 0 . 3125. 2. Exercise 5.16 (a) The mean of X is (15)(0 . 5) = 7 . 5; the mean of ˆ p is 0.5. (b) The mean of X increases with n; it is 75 with n = 150, and 750 with n = 1500. The mean of ˆ p is 0.5 for any value of n. 3. Exercise 5.24 When n = 300, the distribution of ˆ p is approximately Normal with mean 0.49 and standard deviation 0.02886 (nearly twice that in Exercise 5.22). When n = 5000, the standard deviation drops to 0.00707 (less than half as big as in Exercise 5.22). Therefore: n = 300 : P (0 . 46 < ˆ p < . 52) . = P (- 1 . 04 < Z < 1 . 04) . = 0 . 7016 n = 5000 : P (0 . 46 < ˆ p < . 52) . = P (- 4 . 24 < Z < 4 . 24) . = 1 Large samples give a better probability that ˆ p will be close to the true proportion p....
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This note was uploaded on 07/14/2011 for the course ECON 2023 taught by Professor Rush during the Spring '08 term at University of Florida.

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econ310_f09_ps7_ans - Econ 310: Problem Set #7 Solutions...

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