The Centers for Disease Control reported the percentage of people 18 years of ag
ID: 3369034 • Letter: T
Question
The Centers for Disease Control reported the percentage of people 18 years of age and older who smoke (CDC website, December 14, 2014). Suppose that a study designed to collect new data on smokers and nonsmokers uses a preliminary estimate of the proportion who smoke of .27.
a. How large a sample should be taken to estimate the proportion of smokers in the population with a margin of error of .02 (to the nearest whole number)? Use 95% confidence. (1893)
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)? (2747)
c. What is the 95% confidence interval for the proportion of smokers in the population (to 4 decimals)?
Explanation / Answer
a)
ME = 0.02 , p = 0.27
z value at 95% = 1.96
ME = z * sqrt(p * (1-p)/n)
0.02 = 1.96 *sqrt(0.27 * (1-0.27)/n)
n = 1893
b)
p = 520/1893 = 0.2747
the point estimate of the proportion of smokers in the population = 0.2747
c)
CI = p +/- z * ME
= 0.2747 +/- 1.96 * sqrt( 0.2747 * (1-0.2747)/1893)
= (0.2546,0.2948)
The 95% CI is (0.2546,0.2948)
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