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
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Answered question
2021-01-31
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
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:
Step 3
You may compute the sample size at a 95% confidence level as follows:
The value of The number 1.96 corresponds to a 95% confidence level.
=1847.810
Step 4
(b)
Here, X = 520 and n = 1848.
One method for calculating the point estimate is:
=0.2814
Step 5
(c)
The following formula can be used to determine the population's smoking prevalence and its 95% confidence interval:
=(0.2609,0.3019)
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