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Unformatted text preview: Homework Assignment # 6 Exercise Title: Homework No. 6 Date: 5/12/2009 Name (Last, First): Answer Key PID: Section No. of Course: Sections 1 & 2 Sign the Honor Pledge: 6.18 a) 0458 . 100 ) 7 (. 3 . ; 3 . ˆ ˆ = = = = = n pq p p p σ μ b) 015 . 400 ) 9 (. 1 . ; 1 . ˆ ˆ = = = = = n pq p p p σ μ c) 0310 . 250 ) 4 (. 6 . ; 6 . ˆ ˆ = = = = = n pq p p p σ μ 6.19 a) Since the sample sizes are very large, the sampling distributions in Exercise 6.18 will each be approximately normal, with appropriate means and variances. The interval p p ˆ 2 σ ± should cover 95% of the measurements. 6.21 For n = 1000 and p = .1, the sample proportion p ˆ is approximately normally distributed with 0095 . 1000 ) 9 (. 1 . ; 1 . ˆ ˆ = = = = = n pq p p p σ μ a) [ ] [ ] 0174 . 4826 . 5 . 11 . 2 0095 . 1 . 12 . 12 . ˆ = = =  = < z P z P p P b) [ ] [ ] 5 . 0095 . 1 . 10 . 10 . ˆ = < =  = < z P z P p P c) [ ] [ ] 9652 . ) 4826 (. 2 11 . 2 11 . 2 02 . ) ˆ ( 02 . = = ≤ ≤ = ≤ ≤ z P p p P 6.22 The values n pq p / ˆ = σ for n = 100 and various values of p are tabulated and graphed below. Notice that p ˆ σ is maximum for p = .5 and becomes very small for p near 0 and 1. p .01 .10 .30 .50 .70 .90 .99 p ˆ σ .0099 .03 .0458 .05 .0458 .03 .0099 SE p .1 .2 .3 .4 .5 .6 .7 .8 .9 1 .01 .02 .03 .04 .05 6.23 Fir fixed p , n pq p / ˆ = σ . If n is increased, p ˆ σ decreases. Similarly, since n x σ σ = ˆ , the standard deviation of x will decrease as n increases....
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This note was uploaded on 04/14/2008 for the course ECON 400 taught by Professor Turchi during the Spring '08 term at UNC.
 Spring '08
 turchi

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