Question

Suppose a researcher is interested in determining if there is a relationship between low birth weight and pediatric pneumonia. In order to test this relationship, the researcher will use a σ=746 grams and a margin of error plus or minus 646 grams. How many newborns will the researcher need to sample in order to be 95% confident?

Answer 1

Answer:

He will need 4 newborns in the sample to be 95% confident.

Step-by-step explanation:

We have that to find our $\alpha$ level, that is the subtraction of 1 by the confidence interval divided by 2. So:

$\alpha = \frac{1-0.9}{2} = 0.05$

Now, we have to find z in the Ztable as such z has a pvalue of $1-\alpha$.

So it is z with a pvalue of $1-0.05 = 0.95$, so $z = 1.645$

Now, find the margin of error M as such

$M = z*\sqrt{\sigma}{\sqrt{n}}$

In which $\sigma$ is the standard deviation of the population and n is the length of the sample.

So:

$646 = 1.645*\frac{746}{\sqrt{n}}$

$646\sqrt{n} = 1227.17$

$\sqrt{n} = 1.90$

$\sqrt{n}^{2} = (1.90)^{2}$

$n = 3.61$

He will need 4 newborns in the sample to be 95% confident.