Question

We are interested in studying the BMI of group of middle-aged men at risk for developing diabetes mellitus. The standard deviation of the BMI for the population is 2.65 kg/m2. Determine the number of subjects needed to estimate the true mean BMI within 0.75 units using a 95% confidence interval.

What is the sample size needed for the confidence interval estimate? Round up to the next integer.

Answer 1

Solution

standard deviation = =2.65

Margin of error = E = 0.75

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

sample size = n = [Z/2* / E] 2

n = ( 1.96*2.65 / 0.75 )2

n =47.96

Sample size = n =48