Question

Mean birthweight is studied because low birthweight is an indicator of infant mortality. A study of babies in Norway published in the International Journal of Epidemiology shows that birthweight of full-term babies (37 weeks or more of gestation) are very close to normally distributed with a mean of 3600 g and a standard deviation of 600 g. Suppose that Melanie is a researcher who wishes to estimate the mean birthweight of full-term babies in her hospital. What is the minimum number of babies should she sample if she wishes to be at least 90% confident that the mean birthweight of the sample is within 225 grams of the the mean birthweight of all babies? Assume that the distribution of birthweights at her hospital is normal with a standard deviation of 600 g.

Answer 1

we have standard deviation (SD) = 600g, Margin of error(ME) = 225 grams and z score for 90% confidence level is 1.645 (using normal distribution table for 0.10 level)

Using the formula

sample size(n) = [(z*SD)/ME]^2

setting the given values, we get

sample size(n) = [(1.645*600)/225]^2 = (987/225)^2 = 19.24 i.e. 19 babies

so, we need minimum of 19 babies to be at least 90% confident, so that the mean birthweight of the sample will be within 225 grams of the mean birthweight of all babies.