# Proportion Z-score calculator

#### Jaffacakes

##### New Member
Hi! I have a sample (of 30) who’s outcome was measured binomially as either YES/NO. The expected population should have entirely NO answers. I therefore want to calculate if there is a significant difference in the proportions between sample of 23/30 (23-YES, 7-NO) and the expected proportion of 0/30 (0-YES, 30-NO). Is using a z-score calculator and finding the p-value a correct method even when one proportion is 0%? Can this method also be used if the different sample populations were compared with each other (ie 23/30 compared with 15/30)? Thank you!

#### Archidamus

##### Member
The normality assumption is usually reserved for when npq >= 10, where q = 1-p. That's my rule of thumb at least. When you get very high/low p's the distribution is less normal and exact calculations are preferred. I think the way to go about this is to create confidence intervals of p for both samples and see if they overlap.

#### Karabiner

##### TS Contributor
Your Null hypothesis says that your data are collected from a population with a YES proportion of 0.00000000000... .

Obviously, you can reject that hypothesis as soon as you have just 1 YES observed in your sample.

AFAICS it makes no sense to ask how often a 23% rate would be observed in samples of size 30, if the population rate is assumed to be exactely zero.

With kind regards

Karabiner