A social service worker wants to estimate the true proportionof pregnant teenage

Question

A social service worker wants to estimate the true proportionof pregnant teenagers who miss at least one day of school per weekon average. The social worker wants to be within 4% of thetrue proportion when using a 95% confidence interval. Aprevious study estimated the population proportion at 0.28. A. Using this previous study as as estimate for p, whatsample size should be used? B. If the previous study was not available, whatestimate for p should be used? A social service worker wants to estimate the true proportionof pregnant teenagers who miss at least one day of school per weekon average. The social worker wants to be within 4% of thetrue proportion when using a 95% confidence interval. Aprevious study estimated the population proportion at 0.28. A. Using this previous study as as estimate for p, whatsample size should be used? B. If the previous study was not available, whatestimate for p should be used?

Explanation / Answer

Given =0.05, Z(0.025)=1.96 (check normal table) E=0.04, p=0.28 (a) n=(Z/E)^2*p*(1-p) = (1.96/0.04)^2*0.28*(1-0.28) =484.04 Take n=485 (b) Using p=0.5

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