1) 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 90% CI must be no wider than 15.5% to be useful. Given these constraints, the number of children required for the sample is:

2) The ability to taste the compound phenylthiocarbamide (PTC) is a genetically controlled trait in humans. Researchers are planning a study to estimate the proportion of these "tasters." For their purposes a 95% CI must be no wider than 22% to be useful. Given these constraints, the number of people required for the sample is: