The 2003 Statistical Abstract of the United States reported the percentage of pe
ID: 3249539 • Letter: T
Question
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? Use 95% confidence. Remove all commas from your answer before submitting and round up to whole b. Assume that the study uses your sample size recommendation in part (a) and finds 520 smokers. What is the point estimate of the proportion of smokers in the population? (to 4 decimals) c. What is the 95% confidence interval for the proportion of smokers in the population? (to 4 decimals) Enter your answer using parentheses and a comma, in the form (n1, n2).Explanation / Answer
p = 0.30
a)
z value at 95% = 1.96 ME = +/- z * sqrt(p * ( 1 -p) / n)
0.02 = 1.96 * sqrt ( 0.30 * 0.70 / n)
n = 2016.84 = 2017
b)
Point estimate of the proportion smokers in population = 520 / 2017 = 0.2578
c)
z value at 95% = 1.96
CI = p + /- z * sqrt( p * (1 - p) / n)
= 0.2578 + /- 1.96 * sqrt ( 0.2578 * 0.7422 / 2017)
= (0.2387 , 0.2768)
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