I need to be shown the correct statistical method to test two known sample means for difference when 1) the population mean and standard deviation are known, 2) the two sample means and standard deviations are known, and 3) the two sample means are each approximately 50% of the total population.
The actual problem: I have a lage set of test results and my goal is to compare the results for statistical difference based on gender (one tailed test - boys do worse).
1) I need one problem done for me as an example (I have several such tests to compare).
2) I need the formula or a reference to the formula on the web so I can do the balance of the work.
3) I need some evidence to confirm that this methodology is in fact the correct test for these circumstances (again, most likely from the web).
I need this in the next day or so.
Example data are attached.