The first block of output provides some descriptive statistics for the two groups being compared: mean, standard deviation, standard error of the mean.
Tha second block reports informations related to the t-test. Levene test tests if the two groups have variance which is not significantly different (an assumption of t test). Then, the result of the t test are reported (second block-first row), while the results of the Welch t test are reported in the second row. The latter is a 'version' of t test that does not assume equal variance (and that is why the levene test is only reported on the first row).
The mean difference between the two samples is significant, as reported under the header 'sig. (2 tailed)'. Further, the confidence interval for the mean difference between the two samples is reported in the last two columns to the right. By the way, the 95% confidence interval does not comprese zero, which is expected since the difference between the two samples is significant.
Please note that, with that huge sample size, even a small difference is bound to be significant. The evaluation of the 'practical' importante of that small difference is up to you and to the context of your research.
I have trouble seeing the results, but if the t test is signficant the next step is usually to report the effect size (the mean difference between the samples). You would want to comment on whether the difference is substantively large - something which is a substantive not statistical reality. As Gianmarco notes if you have enough power everything is signficant (well a lot of things). The question to ask is if the mean difference is enough to really matter.
Thanks for the responses, and sorry for the delay in my response. I've still having trouble understanding what this output is telling me. I expected it to confirm my thoughts that Charters schools do not meet the needs of socioeconomically disadvantaged students, but I feel like when I'm looking at it, that it is telling me that they are almost the same (their means are both so close together). Could you help me address this thought? Am I looking in the wrong area?
I'm a bit confused on what the dependent variable is. I'm guessing AYP is Adequate Yearly Progress and API is Academic Performance Index, but skimming Wikipedia about those two things, I'm still not sure which one was your dependent variable or why you ended up with group means between 0 and 1.
I expected it to confirm my thoughts that Charters schools do not meet the needs of socioeconomically disadvantaged students, but I feel like when I'm looking at it, that it is telling me that they are almost the same (their means are both so close together). Could you help me address this thought? Am I looking in the wrong area?
it certainly looks like there is almost no difference. You might want to look at the distribution of the groups, i.e are they at least approximatively normally distributed ? If they are strongly skewed then given the imbalance in the sample sizes, you might have some grounds to doubt the test results.
Also, is there any chance of the sampling for either (both) groups being biased?
If everything is all right, you might need to consider that your assumption is not supported by data.