# ismch18 - Chapter 18 Additional Topics in Sampling 137...

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Chapter 18: Additional Topics in Sampling 137 Chapter 18: Additional Topics in Sampling 18-1 through 5 Answers should refer to each of the steps outlined in Figure 18.1 Steps in a sampling study 18-6 through 8. Answers should deal with issues such as (a) the identification of the correct population, (b) selection (Nonresponse) bias, (c) response bias 18.9 While the recall method will lower the number of nonresponses, a bias may be built in since this technique will reduce the participation of individuals who are absent on Thursday evenings (e.g., night students, second shift workers, shopping mall employees, etc.) 18-10 through 13 Within Minitab, go to Calc Make Patterned Data… in order to generate a simple set of numbers of size ‘n’. Then use Calc Random Data… Sample from Columns… in order to generate a simple random sample of size ‘n’. 18-14 9.7, 6.2 x s = = 2 2 ( ) (6.2) 139 ˆ 50 189 x s N n n N σ - = = = .7519 9.7 ± 1.96 (.7519) (8.2262, 11.1738) 18.15 a. 127.43 x = b. 2 2 2 (43.27) 760 ˆ 60 820 x s N n n N σ - = = = 28.9216 c. 127.43 ± 1.645 ( 28.9216 ) (118.5834, 136.2766) d. [137.43 – 117.43]/2 = 10 = /2 28.9216 z α , solving for z: 1.86 tabled value of .9686 yields a confidence interval of 93.72% or an α of .0628 18-16 2 (5.32) 85 ˆ 40 125 x σ = = .6936 7.28 ± 2.58 (.6936) (5.4904, 9.0696) 18-17 a. false: as n increases, the confidence interval becomes narrower for a given N and s 2 b. true c. true: the finite population correction factor is larger to account for the fact that a smaller proportion of the population is represented as N increases relative to n. d. true 18-18 2 2 2 2 ( ) 1 1 ˆ 1 x s N n s n s n N n N n N σ - = = - = -

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138 Instructor’s Solutions Manual for Statistics for Business & Economics, 5 th Edition 18.19 99% confidence interval: / 2 /2 ˆ ˆ x x Nx Z N N Nx Z N α α σ μ σ - < < + where, (189)(9.7) 1833.30 Nx = = 2 2 (6.2) ˆ ( ) 189(189 50) 50 x s N N N n n σ = - = - = 142.1167 1833.30 2.58(142.1167) ± 1466.6390 < N μ < 2199.9610 18.20 95% confidence interval: / 2 /2 ˆ ˆ x x Nx Z N N Nx Z N α α σ μ σ - < < + where (820)(127.43) 104,492.6 Nx = = 2 2 (43.27) ˆ ( ) 820(820 60) 60 x s N N N n n σ = - = - = 4,409.8619 104,492.6 1.96(4409.8619) ± 95,849.2706 < N μ < 113,135.9294 18.21 90% confidence interval: / 2 /2 ˆ ˆ x x Nx Z N N Nx Z N α α σ μ σ - < < + where (125)(7.28) 910 Nx = = 2 2 (5.32) ˆ ( ) 125(125 40) 40 x s N N N n n σ = - = - = 86.7054 910 1.645(86.7054) ± 767.3696 < N μ < 1,052.6304 18-22 x = 143/35 = 4.0857 90% confidence interval: / 2 /2 ˆ ˆ x x Nx Z N N Nx Z N α α σ μ σ - < < + where (120)(4.0857) 490.2857 Nx = = 2 2 (3.1) ˆ ( ) 120(120 35) 35 x s N N N n n σ = - = - = 52.9210 490.2857 1.645(52.9210) ± 403.2307 < N μ < 577.3407 18-23 p = x/n = 39/400 = .0975 [ (1 ) /( 1)][( ) / ] p p p n N n N σ = - - - [(.0975)(.9025) /(399)][(1395 400) /1395] = - = .0125 95% confidence interval: .0975 ± 1.96(.0125): .073 up to .1220 18-24 p = 56/100 = .56
Chapter 18: Additional Topics in Sampling 139 [ (1 ) /( 1)][( ) / ] p p p n N n N σ = - - - [(.56)(.44) /99][(420 100) / 420] = - =.0435 90% confidence interval: .56 ± 1.645(.0435): .4884 up to .6316 18-25 p = 37/120 = .3083 [ (1 ) /( 1)][( ) / ] p p p n N n N σ = - - - [(.3083)(.6917) /(119)][(257 120) / 257] = - = .0309

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