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 99% confident that the mean birthweight of the sample is within 150 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.

n = ?

Answer 1

Mean birth weight = mu = 3600 g

standard deviation of birth weight = SD = 600 g

Confidence interval = 99%

alpha = 1 - 0.99 = 0.01

required condition :  mean birth weight of the sample is within 150 grams

or the difference between mean birth weight and sample size = 150 = | x_bar - mu |

Z_critical at 99% CI for two tailed = 2.58

P[ | x_bar - mu | / ( SD/n^0.5) > Z_critical ] = alpha = 0.01 = P[ 150/( 600/n^0.5) > 2.58 ] = 0.01

or, 150/( 600/n^0.5) > 2.58

150/2.58 > 600/n^0.5

58.139 > 600/n^0.5

squaring both sides

3380.14 > 360000/n

n > 360000/3380.14

n > 106.5

n = 107 at least to obtain 99% confidence interval