STAT100B_HW3S

# STAT100B_HW3S - STAT 100B: Homework 3 Solutions Denise Tsai...

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Denise Tsai January 31, 2011 1. Suppose we roll a die 1000 times, and the average of the 1000 numbers is 3.4. Is there evidence that the die is not fair? Solution: Let the outcome of the roll be X , then ¯ X = 3 . 4. If a die is fair, μ 0 = E ( X ) = 6 X i =1 p i X i = 6 X i =1 i 6 = 3 . 5 σ 2 = V ar ( X ) = 6 X i =1 p i ( X i - μ 0 ) 2 = 6 X i =1 ( i - 3 . 5) 2 6 = 2 . 9167 Hypothesis testing: ( H 0 : μ = 3 . 5 H a : μ 6 = 3 . 5 Z = ¯ X - μ 0 σ n = 3 . 4 - 3 . 5 2 . 9167 1000 = - 1 . 8516 p-val = 2 × 0 . 0322 = 0 . 0644 > 0 . 05 We do not reject the null hypothesis. Therefore, we do not have strong evidence to claim that the die is not fair. 2. Suppose we generate 1000 random numbers using a random number generator in the computer. The random number generator is supposed to output random numbers that are independent and uniformly distributed over [0 , 1]. If the average of these 1000 num- ber is .53. Is there evidence that there is something wrong with this random number generator? 1

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## This note was uploaded on 09/20/2011 for the course STAT 100B taught by Professor Wu during the Winter '11 term at UCLA.

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STAT100B_HW3S - STAT 100B: Homework 3 Solutions Denise Tsai...

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