# Comparing two proportions with Z-test

I am testing splitting phone calls to a service between two IVR menu's to determine which messaging is more effective. 80% to the main IVR menu (Group a) and 20% to an alternative (Group b).

The data I have is Group a: Total calls, Transfer rate (10,000, 15%) and the same for group b (2000, 10%).

I want to determine whether the result is statistically significant.

So H0: No change H1: the change has been effective

As I have two proportions, should I be using a z-score? and can I assume the data is normally distributed with only these proportions?

My working so far is:

p1 = 15%, n = 10,000, sd:SQRT(0.15(1-0.15)/10,000) = 0.00357

p2 = 10%, n = 2,000, sd = 0.00671

z = (0.1-0.15)/0.00671 = -7.4535, pvalue = 3.4^-E13

Is this approach correct? If not, what should I be doing to determine whether the change has been effective?

Thanks

• "Group a: Total calls, Transfer rate (10,000, 15%) and the same for group b (2000, 10%). I want to determine whether the result is statistically significant. " ... if by "result" you mean to ask whether the proportions are more different than could be accounted for by random variation, plainly they are. That much difference with that large a sample size? of course the population proportions are different (unless your significance level is extremely tiny, I guess). Effectiveness would seem to at least be in part a matter of effect size, rather than significance -- I'd focus on tat Jun 2 '17 at 6:56