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ObesityObesity is defined as a body mass index (BMI) of 30
Chapter 7, Problem 18E(choose chapter or problem)
Obesity is defined as a body mass index (BMI) of \(30\mathrm{\ kg}/\mathrm{m}^2\) or more. A 95% confidence interval for the percentage of U.S. adults aged 20 years and over who were obese was found to be 22.4 to 23.5%. What was the sample size?
Source: National Center for Health Statistics (www.cdc.gov/nchs).
Questions & Answers
QUESTION:
Obesity is defined as a body mass index (BMI) of \(30\mathrm{\ kg}/\mathrm{m}^2\) or more. A 95% confidence interval for the percentage of U.S. adults aged 20 years and over who were obese was found to be 22.4 to 23.5%. What was the sample size?
Source: National Center for Health Statistics (www.cdc.gov/nchs).
ANSWER:Step 1 of 2
Our goal is :
We need to find the sample size.
Given the United States aged 20 years and over who ever was found to be 22.4 to 23.5.
So, \(22.4<p<23.5\)
From the given information we know that confidence interval C is 95%.
Now we have to find the margin of errors.
The margin of error is half the width of the confidence interval:
\(\begin{array}{l} E=\frac{23.5 \%-22.4 \%}{2} \\ E=\frac{1.1 \%}{2} \\ E=0.55 \% \\ E=0.0055 \end{array}\)
When \(\widehat{p}\) known then the sample size formula is
\(n=\frac{\left[z_{\alpha / 2}\right]^{2}}{E^{2}} \times \widehat{p} \widehat{q}\)
When \(\widehat{p}\) unknown then the sample size formula is
\(n=\frac{\left[z_{\alpha / 2}\right]^{2}}{E^{2}} \times 0.25\)