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# Homework 2 - 550.430 Introduction to Statistics Spring 2010...

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550.430 Introduction to Statistics Spring 2010 Naiman Homework #2 Due Monday Feb 13th (1) Chapter 7 #24 (2) Chapter 7 #35 (3) Chapter 7 #37 (4) Suppose we estimate the mean income μ for people living in some city using an esti- mator ˆ μ with the property that ˆ μ N ( μ, σ 2 ) . (a) What is the probability that ˆ μ < μ + . 75 σ ? (b) What is the probability that ˆ μ > μ + 1 . 25 σ ? (c) What is the probability that μ + . 60 σ < ˆ μ < μ + . 75 σ ? (d) What is the probability that μ - . 60 σ < ˆ μ < μ + . 75 σ ? (e) What is the probability that | ˆ μ - μ | < σ ? (5) Suppose we estimate the mean height of μ for people living in some city using an estimator ˆ μ. We also estimate the standard deviation σ ˆ μ of the estimator using an estimator denoted by s ˆ μ . Assume that the quantity ˆ μ - μ s ˆ μ is distributed as Student’s t with 10 degrees of freedom. (a) What is the probability that ˆ μ > μ + 1 . 812 s ˆ μ ? (b) What is the probability that | ˆ μ - μ | < 1 . 812 s ˆ μ (6) (Use of Chebychev’s inequality) Consider estimation of a population mean μ whose

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