Vitamin D is an essential ingredient for maintaining strong

Vitamin D is an essential ingredient for maintaining strong bones and teeth. Sources of this vitamin are natural sunlight and certain dietary supplements. There is a growing concern among pediatricians that today\'s youngsters are spending too much time indoors. This increases the risk of vitamin D deficiency and all of its related health issues. A research team would like to estimate the proportion of children (aged 6 to 12) that currently exhibit a deficiency in this micro-nutrient. For their purposes a 99% CI must be no wider than 10% to be useful. Given these constraints, the number of children required for the sample is:

Solution

n = (Z / E)^2 * p * (1-p)

Z for 95% CI = 1.96

because , alpha = 1 - 0.95 = 0.05 nad P(Z > 1.96) = 0.05/2

p= 0.5 (if unknown)

so , n = (1.96 / (0.095/2))^2*0.5*(1-0.5) = 426 (round up)