Expert answers to "The Centers for Disease Control reported the percentage..."

Nannie Mack

Answered question

2021-03-02

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 0.30. a. How large a sample should be taken to estimate the proportion of smokers in the population with a margin of error of 0.02? Use 95% confidence.

Answer & Explanation

BleabyinfibiaG

Skilled2021-03-03Added 118 answers

Step 1
Solution:
a.
From the given information, confidence level is $0.95, p = 0.30 a n d E = 0.02 .$
$1 - α = 0.95$
$α = 1 - 0.95$
$α = 0.05$
Step 2
Then,
$n = {(\frac{Z_{\frac{α}{2}}}{E})}^{2} p (1 - p)$
$= {(\frac{Z_{\frac{0.05}{2}}}{0.02})}^{2} 0.30 (1 - 0.30)$
$= {(\frac{Z_{0.025}}{0.02})}^{2} (0.21)$
$= {(\frac{1.96}{0.02})}^{2} (0.21) [U \sin g e x c e l f u n c t i o n = N O R M . I N V (0.025, 0, 1)]$
$= 2016.84$
$\approx 2017$
Thus, the required sample size is 2017.

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