Homework100B3

Homework100B3 - 165 185. Let us assume that the heights of...

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STAT 100B HW 3 Due Friday 5pm Problem 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? Problem 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 number is .53. Is there evidence that there is something wrong with this random number generator? Problem 3: Suppose we randomly sample 10 people from the population of adult males, and we measure their heights. Suppose the heights (in the unit of cm) are 182 166 187 196 173 188 192 164
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Unformatted text preview: 165 185. Let us assume that the heights of the population follow a normal distribution N ( μ,σ 2 ). (1) Calculate the sample variance s 2 . (2) Test the hypothesis H : μ = 180 versus H 1 : μ > 180. (3) Find the 95% confidence interval for the average height of the population. Problem 4: Suppose X 1 ,...,X n ∼ f ( x ) independently. Let μ = E[ X ], and σ 2 = Var[ X ]. Let ¯ X = 1 n n X i =1 X i , and s 2 = 1 n-1 n X i =1 ( X i-¯ X ) 2 . Prove E[ ¯ X ] = μ , Var[ ¯ X ] = σ 2 /n , and E( s 2 ) = σ 2 . 1...
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This note was uploaded on 03/30/2011 for the course STAT 100B taught by Professor Wu during the Spring '11 term at UCLA.

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