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I used my calculator to do a two tailed Z test for two proportions. Here's the data I input:

X1 is  834
n1 is 3610
X2 is  145
n2 is  495

I chose p1 not equal to p2
I set alpha to 0.05

My hypotheses are:
$H_0: \pi_1= \pi_2$
$H_a: \pi_1 \neq \pi_2$

The calculated Z score is $-3.03$, which gives a $p = .002$, so I am rejecting the null.

Here is my question: what does the negative Z score mean:

a) that the $X_1/n_1$ proportion is > than the $X_2/n_2$ proportion? OR
b) that the $X_2/n_2$ proportion is > than the $x_1/n_1$ proportion?

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    $\begingroup$ You can calculate which of the two sample proportions is larger. It's not going to lead you to conclude the population proportions differ in the opposite direction. $\endgroup$
    – Glen_b
    Jul 20, 2017 at 3:16
  • $\begingroup$ If the one sided p-value is 0.002 the two-sided p-value is 0.004 approximately. $\endgroup$
    – Michael R. Chernick
    Jul 20, 2017 at 5:13
  • $\begingroup$ Thank you but I still don't understand. Since the difference is significant based on the score, can I say that the x1/n1 proportion is greater than the X2/n2 proportion? I am just trying to understand what it means to get a negative Z score. Thanks. I am just 17 and trying to learn. $\endgroup$
    – JHB
    Jul 20, 2017 at 12:24

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