Interpreting R results proportions test

I hope someone can help me. I'm really bad at statistics and the funny thing is that I'm a researcher so I have to understand them. My problem is that I never know how to interpret the results. This is what R software gives me:

2-sample test for equality of proportions with continuity correction

data: c(21, 239) out of c(36, 882)
X-squared = 15.1204, df = 1, p-value = 1
alternative hypothesis: less
95 percent confidence interval:
-1.0000000 0.4641915
sample estimates:
prop 1 prop 2
0.5833333 0.2709751

Now, my stats guy here told (and I rather not ask him again the same thing) that if my p-value was anywhere above 0.05 I should accept the null hypothesis and accept the alternative hypothesis. So if I get p-value = 1, according to my own alternative hypothesis, would that mean that there are no significant differences between my two samples? Let me know, because I intuitively expected quite the opposite.

Thanks a lot for any help.


TS Contributor
I'm not sure what's so funny about a "researcher" knowing nothing about statistics....:D

What were the sample sizes for each proportion?

So, proportion 1 was approx 0.583 and proportion 2 was 0.271?

What does this mean?
data: c(21, 239) out of c(36, 882)