Going in, we were hoping to see that the proportion of students who own an Android vs. those who own an iPhone was pretty consistent with the national average (0.45 Android vs 0.55 for iPhone). As it turned out, this was not the case. In fact, our total proportions were off by approximately 0.15. iPhone was larger (just like it was nationally), but by a much larger margin. We tested the null hypothesis that our overall proportion for Android was 0.45. We rejected the null hypothesis at the 0.05 level of significance because our p-value of 0.024 was less than alpha. Therefore, there was sufficient evidence to say that the true proportion of students at NOHS who own an Android was less than 0.45.
When looking closer, however, there might have been a potential reason for this. The proportion for girls was substantially one-sided for iPhone. This threw the overall proportion out of line. The overall proportions for boys were only 0.015 off from the hypothesized values. We tried to test the hypothesis that the proportion of Android for boys was greater than that for girls, but our test was invalid; we needed a larger sample in order to meet the assumption that n times p was greater than 10 for girls. Had we met this conclusion, we most likely would have rejected the null hypothesis (when continued, we got a p-value less than alpha).
Our random sample gave us some very insightful data about phone ownership at our high school.
In conclusion, our study revealed that the proportion of iPhone users at North Olmsted High School was much larger than that of Android users. You win this time, Steve Jobs.