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 to be .30. a) How large a sample should be taken to estimate the proportion of smokers in the population with a margin of error of 2%? Use 95% confidence. b) Assume that the study uses your sample size recommendation above and finds 520 smokers. What is the point estimate of the proportion of smokers in the population? c) What is the 95% confidence interval for the proportion of smokers in the population?

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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 to be .30.  a) How large a sample should be taken to estimate the proportion of smokers in the population with a margin of error of 2%? Use 95% confidence.  b) Assume that the study uses your sample size recommendation above and finds 520 smokers. What is the point estimate of the proportion of smokers in the population?  c) What is the 95% confidence interval for the proportion of smokers in the population?

Tasneem Almond · Accepted Answer

Step 1  Given data  Error = 0.02  Confidence level = 0.95  Significance level =α=1−0.95=0.05  Z0.052=Z0.025=±1.96  (From Excel = NORM.S.INV(0.025))  sample proportion(p)=0.30  a)  Sample size is given by(n)  Margin of error formula is given by  E=Zα2×p−(1−p)n  Simplifying the above formula  n=p(1−p)×(Zα2E)2=0.3×(1−0.3)×(1.960.02)2=2016.84≈2017  Step 2  b)  n=2017  No of smokers = 520  Point estimate is given by  p^=5202017=0.258  Step 3   c)  95% confidence interval for the proportion of smokers in the population is given by  Confidence level = 0.95  Significance level =α=1−0.95=0.05  Z0.052=Z0.025=±1.96  (From Excel = NORM.S.INV(0.025))  Confidence interval is given by  p^+Zα2p^−(1−p^)n=0.258±1.960.258(1−0.258)2017=(0.239,0.277)  Step 4  Result:  a) 2017  b) 0.258  c) (0.239,0.277)

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 designe

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