Question

What are the conditions for using the normal approximation for a sampling distribution of proportions?

Answer 1

Hello, Howard!

I Googled "normal approximations from sample proportions" and came up with the following result, among many:

https://onlinecourses.science.psu.edu/stat200/node/43

In particular, have a look at this:

np≥10 and n(1−p)≥10.

n=sample size
p=sample proportion

Answer 2

Take n and p from the problem statement and determine whether or not the two inequalities shown above are true for those values.

Answer 3

One way to do this...

if \(p\pm3\sqrt{pq/n}\) lie within (0,1)

then \(0<p-3\sqrt{pq/n}\) and \(p+3\sqrt{pq/n}<1\)

this is equivalent to \(n>9\left(\dfrac{p}{q}\right)\) and \(n>9\left(\dfrac{q}{p}\right)\)

so you want \[n>9\left(\frac{\max(p,q)}{\min(p,q)}\right)\]

Answer 4

Ok guys, but i dont understand how i wrtie out these answers in sentence forms

Answer 5

sorry cant help with this one