Question

Obesity if dened as a body mass index (BMI) of 30 kg/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 16.5% to 27.5%. What was the sample size used?

Answer 1

Solution :

Point estimate = = (Lower confidence interval + Upper confidence interval ) / 2

Point estimate = = (0.165+0.275) / 2=0.22

Margin of error = E = Upper confidence interval - = 0.275-0.22=0.055

= 0.22

1 - = 1 - 0.22= 0.78

margin of error = E = 0.055

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96 ( Using z table )

Sample size = n = (Z/2 / E)2 * * (1 - )

= (1.96 / 0.055)2 * 0.22 * 0.78

= 217.9

Sample size =218