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
pancha3
Answered question
2021-01-15
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?
Answer & Explanation
Tasneem Almond
Skilled2021-01-16Added 91 answers
Given data
Error = 0.02
Confidence level = 0.95
Significance level
(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
Simplifying the above formula
Step 2
b)
n=2017
No of smokers = 520
Point estimate is given by
Step 3
c)
95% confidence interval for the proportion of smokers in the population is given by
Confidence level = 0.95
Significance level
(From Excel = NORM.S.INV(0.025))
Confidence interval is given by
Step 4
Result:
a) 2017
b) 0.258
c) (0.239,0.277)
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