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

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

Explanation:

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

`\alpha = (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*√(\sigma){√(n)}`

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

So:

`646 = 1.645*(746)/(√(n))`

`646√(n) = 1227.17`

`√(n) = 1.90`

`√(n)^(2) = (1.90)^(2)`

`n = 3.61`

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