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I want to find out if 2 proportions are different or not.

For one, sample size is <30.

For the other, it's much >30.

Can I use the Z test since one size is large? Or do i have to use the t test? Or can I not compare since the numbers are very different? I'd be grateful for any help. Thanks.

viktor nikiforov
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As you can learn from this answer

T-values are used for inference with means because the sample standard deviation has to be used as an estimate for a population standard deviation, rather than using the population standard deviation directly (this is generally unknown).

Proportions are a little different in that the standard deviation of the hypothetical curve with mean $ p $ can be calculated by $ \sqrt{\frac{p(1-p)}{n}} $. [...]

So for proportion, the standard deviation is not unknown, which means that you should use the $Z$-test.

However, more likely you should rather use the Pearson's $\chi^2$ test (implemented in prop.test in R) or the exact binomial test (binom.test in R).

Tim
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