This question comes from a practice exam, the following contains the question and the answer provided. However my teachers for this exam are non-respondent and I really need someone to please help explain this to me. I attach the answer below as well.
In an agricultural trial, yields are recorded for samples of plants from four different varieties of a crop:
Variety A: 15, 14, 12, 13
Variety B: 11, 18, 13
Variety C: 18, 25, 19, 20
Variety D: 19, 20, 24
It is revealed that varieties C and D were genetically modified (GM) plants. Varieties A and B were not. By fitting an appropriate model to the data, test the hypothesis:
H0: The mean yields of the two GM varieties are equal and the mean yields of the two non-GM varieties are equal.
My questions are: - Where this equation for F comes from. I understand the need to test for it, but in my experience it is calculated from doing (MS Variable / MS Error). What the values of p_f and p_r represent?
My rationale for the latter is that they represent the upper limits of i from the "appropriate model". If anyone could explain this to me then that would be very much appreciated.
Thank you.
What would be the point in calculating the differences in i values?