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.

Answer 1

n=((z*σ)/m)^2

• n = sample size

• z = t-distributions table value

• σ = Standard deviation

• m = margin of error

n = ( (1.96*600)/100))^2

n = (1176/100)^2

n = (11.76)^2

n = 138.29 --> Ceiling Function (Round to Highest whole integer value)

n = 139

Answer 2

The following information is provided,
Significance Level, α = 0.01, Margin or Error, E = 150, σ = 600

The critical value for significance level, α = 0.01 is 2.58.

The following formula is used to compute the minimum sample size required to estimate the population mean μ within the required margin of error:
n >= (zc *σ/E)^2
n = (2.58 * 600/150)^2
n = 106.5

Therefore, the sample size needed to satisfy the condition n >= 106.5 and it must be an integer number, we conclude that the minimum required sample size is n = 107
Ans : Sample size, n = 107