Confidence Intervalls

H, I have a question where I am not sure if what I calculated is correct.

So there are two therapies, A and B with 48/60 and 25/40 being healed respectively. I shall calculate the 95% CI

I now should calculate the confidence Intervalle for the difference of „proportions“ ( not sure what the English term is, i tried to look it up, but cant find anything useful) I am using the formula

$$(p_1-p_2 )+-Q_(1-\alpha/2)(N(0,1))* \sqrt{p_1(1-p_1)/n_1 + p_2(1-p_2)/n_2}$$

I am still getting used to math Jax....

So that would give me (-1/200, 71/200) And that negative sign just makes no sense imho. How can a proportion be negative.... but i cant find where i made the mistake....

I would be so grateful for your help :)

• The confidence interval depends on the distribution of probabilities. By considering a normal variable for something that is supposed to be limited to (0, 1), then you get errors because the Gaussian law can take any value, not just in (0, 1). – Matthieu Brucher Dec 21 '18 at 11:53
• Hmm, ok, to be honest our professor just gave us this formula and we are supposed to use it. How would i do it differently? I don’t have very much knowledge to start with. It’s an intro course and all we got in the handout and in the lecture is this formula and 3 more for other CI. I am somewhat lost... – Lillys Dec 21 '18 at 12:18