# Thread: Z-test vs. t-test and calculating std error

1. ## Z-test vs. t-test and calculating std error

Hello,

I have two questions concerning proportions.

First, say I have one sample of 1000 units and 10 percent have the characteristic A while 8 percent have B - how would I test whether these two proportions are significantly different, is A actually more common than B? I understand that I can compute a z-test, but how would I calculate the standard error for this test?

What I can find (say, Agresti & Finlay) either seems to describe comparing a proportion in one sample to some population parameter my, or comparing proportions from two different samples – but in my case, I'm dealing with one sample only.

And more generally, is it correct that when comparing proportions I would use a z-test, not a t-test (if I'm wrong, how would I compute the standard error in a t-test?).

For any help, thanks in advance,
deenha

2. Originally Posted by deenha
Hello,

I have two questions concerning proportions.

First, say I have one sample of 1000 units and 10 percent have the characteristic A while 8 percent have B - how would I test whether these two proportions are significantly different, is A actually more common than B? I understand that I can compute a z-test, but how would I calculate the standard error for this test?

What I can find (say, Agresti & Finlay) either seems to describe comparing a proportion in one sample to some population parameter my, or comparing proportions from two different samples – but in my case, I'm dealing with one sample only.

And more generally, is it correct that when comparing proportions I would use a z-test, not a t-test (if I'm wrong, how would I compute the standard error in a t-test?).

For any help, thanks in advance,
deenha
Think $\displaystyle \chi ^2$ test, you have an observed distribution $\displaystyle 100,\ 80,\ 820$ for the three outcomes A, B and C (neither of A or B). Under your null hypothesis the expected distribution is $\displaystyle 90,\ 90,\ 820$.

CB