420Hw01ans - STAT 420 (due Friday, January 25, by 4:00...

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Homework #1 Spring 2008 (due Friday, January 25, by 4:00 p.m.) 1. The salary of junior executives in a large retailing firm is normally distributed with standard deviation σ = $1,500. If a random sample of 25 junior executives yields an average salary of $16,400, what is the 95% confidence interval for μ , the average salary of all junior executives. σ = $1,500, n = 25, X = $16,400. n z 2 X α ± 95% confidence, = 0.05, z 0.025 = 1.960. 25 500 , 1 960 . 1 400 , 16 ± 16,400 ± 588 ( 15,812 , 16,988 ) 2. Redo Problem 1 without assuming that the population standard deviation is known. You are given s = $1,575. s = $1,575, n = 25, X = $16,400. ( ) n t n s 1 2 X - ± 95% confidence, = 0.05, t 0.025 ( 24 ) = 2.064. 25 575 , 1 064 . 2 400 , 16 ± 16,400 ± 650.16 ( 15,749.84 , 17,050.16 ) 3. A cereal packaging machine is supposed to turn out boxes that contain 20 oz of cereal on the average. Past experience indicates that the standard deviation of the content weights of the packages turned out by the machine is σ = 0.25 oz. We wish to test H 0 : μ = 20 vs. H a : μ < 20. If a sample of n = 20 items has mean weight x = 1.79.
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This note was uploaded on 02/10/2009 for the course STAT 420 taught by Professor Stepanov during the Spring '08 term at University of Illinois at Urbana–Champaign.

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420Hw01ans - STAT 420 (due Friday, January 25, by 4:00...

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