Question

A doctor at a local hospital is interested in estimating the birth weight of infants. How large a sample must she select if she desires to be 99% confident that the true mean is within 3 ounces of the sample mean? The standard deviation of the birth weights is known to be 5 ounces.

Answer 1

Answer: 18

Step-by-step explanation:

Given : Margin of error = 3 ounces

Significance level : $\alpha = 1-0.99=0.1$

Critical value : $z_{\alpha/2}=2.576$

Standard deviation :$\sigma=5\text{ ounces}$

The formula to calculate the sample size is given by :-

$n=(\dfrac{z_{\alpha/2}\ \sigma}{E})^2$

$\Rightarrow\ n=(\dfrac{2.576\times5}{3})^2\\\\\Rightarrow\ n=18.4327111111\approx18$

Hence, the minimum sample size should be 18.