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61. The 2003 Statistical Abstract of the United States reported the percentage of people 18 years of age and older who smoke. Suppose that a study designed to collect new data on smokers and nonsmokers uses a preliminary estimate of the proportion who smoke of .30. a. How large a sample should be taken to estimate the proportion of smokers in the population with a margin of error of .02

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JeanaShupp

Answer: Required minimum sample size = 2017

Step-by-step explanation:

Formula : Sample size(n) for population proportion(p):

[tex]n= p(1-p)(\frac{Z^c}{E})^2[/tex] , where E = Margin of error

If p = proportion of smokers

Given: p =0.30 and E=0.02

[tex]z^c[/tex] for 95% confidence level = 1.96

So,

[tex]n=0.30(1-0.30)(\dfrac{1.96}{0.02})^2\\\=0.30(0.70)(98)^2\\\\=2016.84\approx2017[/tex]

Hence, required minimum sample size = 2017

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