# 09_28_09ans - STAT 409 Fall 2009 Examples for The sample...

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STAT 409 Examples for 09/28/2009 Fall 2009 The sample proportion : n x p = ˆ where x is the number of elements in the sample found to belong to the category of interest (the number of "successes"), and n is the sample size. E( P ˆ ) = p , Var( P ˆ ) = ( 29 n p p - 1 , SD( P ˆ ) = ( 29 1 n p p - . A large-sample confidence interval for the population proportion p is n p p z p - ± ˆ ˆ ˆ 1 α 2 . 1. Just prior to an important election, in a random sample of 749 voters, 397 preferred Candidate Y over Candidate Z. Construct a 90% confidence interval for the overall proportion of voters who prefer Candidate Y over Candidate Z. X = 397. n = 749. 749 397 X p ˆ = = n = 0.53 . The confidence interval : n ) p ˆ 1 ( p ˆ z p ˆ 2 - ± α . 90% confidence level α = 0.10 α 2 = 0.05 . 2 z α = 1.645 . 749 ) 47 0 )( 53 0 ( 645 1 53 0 . . . . ± 0.53 ± 0.03 ( 0.50 , 0.56 ) Upper-tail probability 0.25 0.20 0.15 0.10 0.05 0.025 0.02 0.01 0.005 0.0025 0.001 0.0005 z 0.674 0.841 1.036 1.282 1.645 1.960 2.054 2.326 2.576 2.807 3.091 3.291 50% 60% 70% 80% 90% 95% 96% 98% 99% 99.5% 99.8% 99.9% Confidence level

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2. An article on secretaries' salaries in the Wall Street Journal reports: "Three-fourth of surveyed secretaries said they make less than \$25,000 a year." Suppose that the
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09_28_09ans - STAT 409 Fall 2009 Examples for The sample...

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