Question

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

Answer 1

Answer: Required minimum sample size = 2017

Explanation:

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

`n= p(1-p)((Z^c)/(E))^2` , where E = Margin of error

If p = proportion of smokers

Given: p =0.30 and E=0.02

`z^c` for 95% confidence level = 1.96

So,

`n=0.30(1-0.30)((1.96)/(0.02))^2\\\=0.30(0.70)(98)^2\\\\=2016.84\approx2017`

Hence, required minimum sample size = 2017