two tailed hypothesis for difference in proportion mean
hello. i have been doing some problems with hypothesis testing of proportions. i have now a real-world problem and want to make sure i set it up correctly. say i have 2 observed proportion samples:
s1: 100 tests, 25 positives
s2: 100 tests, 23 positives
i'd like to answer 1 questions:
what's the probability that the population from which s1 is drawn has a greater mean than the mean of the population from which s2 is drawn?
here's how i set it up and ran it:
first i ran a sequence of two-tailed proportion tests starting at a significance level of 0.05 and ending at 0.95. i find that they are different at the level of 0.75 of significance (not very significant, i understand). main question to start is, does this mean we are about 25 % confident the means of the 2 populations are different from each other? (null hypothesis having been that the population means are equal). so, call this significance level L1.
then, my next test was to run a one tailed test. the null hypothesis of this one is s2's population mean is >= s1's. this i find we can reject the null hypth at the 0.4 level. can we call this effectively a 60% probability?
then, use a conditional probability statement to answer the question in full - there is a 25% probability they're different, and given the condition they are different, there is a 60% probability s1's population is greater, the answer to the overall statement is: the probability s1's population's mean is greater than s2's is 24%.
am i thinking about this right, or mixing concepts up by using the significance level as a proxy for probability within a conditional probability problem???