Vitamin D is an essential ingredient for maintaining strong bones and teeth. Sou

Question

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 95% CI must be no wider than 14.5% to be useful. Given these constraints, the number of children required for the sample is:

Explanation / Answer

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 95% CI must be no wider than 14.5% to be useful. Given these constraints, the number of children required for the sample is:

P=0.5 ( assuming equal proportion)

For 95%, z=1.96

d=0.145

Sample size = (z2*p*(1-p))/d2

= (1.962*0.5*0.5)/0.1452

=45.67

The sample size required= 46

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