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

generals336

Answered question

2021-01-31

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)?

Answer & Explanation

avortarF

avortarF

Skilled2021-02-01Added 113 answers

Step 1 
Given: 
Error margin (E) equals 0.02
Level of confidence: 95%
Population proportion (p) = 0.26 
Step 2 
(a) 
The following formula could be used to determine the sample size:
n=p(1p)(Zα2E)2 
Step 3 
You may compute the sample size at a 95% confidence level as follows:
The value of Zα2 The number 1.96 corresponds to a 95% confidence level.
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. 
One method for calculating the point estimate is:
p^=Xn 
=5201848 
=0.2814 
Step 5 
(c) 
The following formula can be used to determine the population's smoking prevalence and its 95% confidence interval:
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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