Help! 1. A researcher wishes to estimate , with 90%confidence, The proportion of
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Help! 1. A researcher wishes to estimate , with 90%confidence, The proportion of adults who have high-speed internetaccess. Her estimate must be accurate within 5% of theproportion. a. What the minimum sample size needed,using a prior study that found that 40% of the respondents saidthey have high-speed internet access. b. No preliminary estimate is available.Find the minimum sample size needed. n = (Round up to the nearest whole numberas needed.) 2. An election poll reported that a candidate hada approveal rating 56% with a margin of error E of 5%. Construct aconfidence interval for a proportion of adults who approve of thecandidate. The confidence interval for the proportionof adults who approve of the candidate is. (Round to two decimalplaces as needed.) 3. Construct the indicated confidence interval for thepopulation mean using a T- distribution. C=0, 50,x=110,5=10,n=28 The confidence interval is= (Round the final answer to the nearest tenth as needed.Round all intermediate values to the nearest thousandth asneeded.) 4. A researcher wishes to estimate, with 99%confidence, the percentage of adults who support abolishing thepenny. His estimate must be accurate within 3% of the trueproportion. a. What is the mimimum samplesize needed, using a prior study that found that 25% of therespondends said they support abolishing the penny. b. No priliminary estimate isavailable, Find the mimimum sample size needed. n= (Round up to the nearest whole number as needed.) Help! 1. A researcher wishes to estimate , with 90%confidence, The proportion of adults who have high-speed internetaccess. Her estimate must be accurate within 5% of theproportion. a. What the minimum sample size needed,using a prior study that found that 40% of the respondents saidthey have high-speed internet access. b. No preliminary estimate is available.Find the minimum sample size needed. n = (Round up to the nearest whole numberas needed.) 2. An election poll reported that a candidate hada approveal rating 56% with a margin of error E of 5%. Construct aconfidence interval for a proportion of adults who approve of thecandidate. The confidence interval for the proportionof adults who approve of the candidate is. (Round to two decimalplaces as needed.) 3. Construct the indicated confidence interval for thepopulation mean using a T- distribution. C=0, 50,x=110,5=10,n=28 The confidence interval is= (Round the final answer to the nearest tenth as needed.Round all intermediate values to the nearest thousandth asneeded.) 4. A researcher wishes to estimate, with 99%confidence, the percentage of adults who support abolishing thepenny. His estimate must be accurate within 3% of the trueproportion. a. What is the mimimum samplesize needed, using a prior study that found that 25% of therespondends said they support abolishing the penny. b. No priliminary estimate isavailable, Find the mimimum sample size needed. n= (Round up to the nearest whole number as needed.)Explanation / Answer
(1) (a) Given =0.1, Z(0.05)=1.645 (check normal table),E=0.05 p=0.4 n=(Z/E)^2*p*(1-p) =(1.645/0.05)^2*0.4*(1-0.4) =259.7784 Take n=260 (b) p=0.5 n=(Z/E)^2*p*(1-p) =(1.645/0.05)^2*0.5*(1-0.5) = 270.6025 Take n=271 ----------------------------------------------------------------------------------------- (2) Given p=0.56, E=0.05 The CI is p± E --> 0.56 ± 0.05 --> (0.51, 0.61) ----------------------------------------------------------------------------------------- (4)Given =0.01, Z(0.005)=2.58 (check normal table) E=0.03 (a) p=0.25 n=(Z/E)^2*p*(1-p) =(2.58/0.03)^2*0.25*(1-0.25) = 1386.75 Take n=1387 (b) p=0.5 n=(Z/E)^2*p*(1-p) =(2.58/0.03)^2*0.5*(1-0.5) = 1849 Take n=1849
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