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

generals336 2021-01-31 Answered
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 Questions Navigation Menu preliminary estimate of the proportion who smoke of .26.
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.
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)?
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Expert Answer

avortarF
Answered 2021-02-01 Author has 113 answers
Step 1
Given:
Margin of error (E) = 0.02
Confidence level = 95%
Population proportion (p) = 0.26
Step 2
(a)
The sample size could be calculated using the following formula:
n=p(1p)(Zα2E)2
Step 3
The sample size at 95% confidence level can be calculated as:
The value of Zα2 corresponding to 95% confidence level is 1.96
n=p(1p)(Zα2E)2
=0.26(10.26)(1.960.02)2
=0.1924×9604
=1847.810
1848
Step 4
(b)
Here, X = 520 and n = 1848.
The point estimate can be calculated as:
p^=Xn
=5201848
=0.2814
Step 5
(c)
The 95% confidence interval for the proportion of smokers in the population can be calculated as:
CI=p^±Zα2p^(1p^)n
=0.2814±1.96×0.2814(10.2814)1848
=0.2814±0.0205
=(0.2609,0.3019)
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