The correct formula for magnesium oxide is MgO. This is because Mg forms a +2 ion and O forms a -2 ion. The ions will combine to produce a compound which is neutral (no charge).
A common chemistry experiment many students carry out can determine the empirical formula by allowing magnesium metal to react with oxygen. The reaction is sped up by heating the sample in a crucible. See the video below-
video from: Noel Pauller
If you analyze the data from such an experiment and obtain a 3:2 ratio of Mg to O, this means that the amount of oxygen in the collected product is lower than what is expected.
This could have happened for a couple of different reasons.
If the reaction was allowed to proceed in an uncovered crucible, you would have seen smoke (actually MgO) leaving the container. This would result in decreased mass of the final product.
If the reaction is not allowed to go all the way to completion, then some magnesium will not have reacted, so the final mass of MgO will be lower than what it should have been.
A 3:2 ratio is not an uncommon result for students to obtain when conducting this experiment.
Hope this helps!
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