4. Aresearcher wishes to estimate, with 95% confidence, theproportion of adults

Question

4. Aresearcher wishes to estimate, with 95% confidence, theproportion of adults wheo have high speed Internet access. Herestimate must be accurate with 2% of the true proportion. a.Find the minimum sample size needed, using a prior studythat found that 36% of the respondents said they have high -speedInternet access. b.No preliminary estimate is available. Find the minimumsample size needed. a.What is the minimum sample size needed using a prior studythat found that 36% of the respondents said they have high-speedInternet access? n=______ Round up to the nearest whole number as needed. b. What is the minimum sample size needed assuming that nopreliminary estimate is available? n=______ Round up to the nearest whole number as needed 4. Aresearcher wishes to estimate, with 95% confidence, theproportion of adults wheo have high speed Internet access. Herestimate must be accurate with 2% of the true proportion. a.Find the minimum sample size needed, using a prior studythat found that 36% of the respondents said they have high -speedInternet access. b.No preliminary estimate is available. Find the minimumsample size needed. a.What is the minimum sample size needed using a prior studythat found that 36% of the respondents said they have high-speedInternet access? n=______ Round up to the nearest whole number as needed. b. What is the minimum sample size needed assuming that nopreliminary estimate is available? n=______ Round up to the nearest whole number as needed

Explanation / Answer

Given =0.05, |Z(0.025)|=1.96 (check normal table) E=0.02 -------------------------------------------------------------- (a) p=0.36 n=(Z/E)^2*p*(1-p) =(1.96/0.02)^2*0.36*(1-0.36) =2212.762 Take n=2213 -------------------------------------------------------------- (b) p=0.5 n=(Z/E)^2*p*(1-p) =(1.96/0.02)^2*0.5*(1-0.5) =2401 Take n=2401

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