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Unformatted text preview: STAT 400 Examples for 11/01/2011 (2) Fall 2011 The sample proportion : n x p = 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 ) = p , Var( P ) = ( ) n p p 1 , SD( P ) = ( ) 1 n p p . A largesample confidence interval for the population proportion p is n p p z p  1 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 = = n = 0.53. The confidence interval : n ) p 1 ( p z p 2 . 90% confidence level = 0.10 2 = 0.05. 2 z = 1.645. 749 ) 47 )( 53 ( 645 1 53 . . . . 0.53 0.03 ( 0.50 , 0.56 ) Uppertail 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 1 . Let X have a Binomial distribution with parameters n and p . Recall that ( ) 1 X p p n p n has an approximate Standard Normal N ( 0, 1 ) distribution, provided that n is large enough, and ( )  < < 1 1 X P 2 2 z p p n p n z . Show that an approximate 100 ( 1 ) % confidence interval for p is ( ) n z n z n p p z n z p 2 2 2 2 2 2 2 2 1 4 1 2 + + + , where n p X = ....
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 Fall '08
 Kim
 Statistics, Probability

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