That is a good question, but the answer does not depend on the A-values. That is, if you were to compare the preferred conformations of 1-methylcyclohexanol, then it would be as predicted, axial OH. However, that is not the question in this case.
The question asks for you to predict the product ratio of a reaction. The product would have two equatorial substitutents in the preferred conformation. That gives two choices, either the OH or the CH3 is axial. However, this is a reaction. The question is, "Will the preferred conformation (axial OH) lead to the most stable product?" Because the product is a tertiary alcohol in sulfuric acid, I argue the reaction can equilibrate to the most stable product. Therefore, I can imagine two factors involved. First, the group at equilibrium is not necessarily an ROH, but rather an ROH2(+). Secondly, the rate of elimination of water from axial and equatorial should also be considered. If the elimination of an axial water is much faster than equatorial, then the equilibrium would result in the equatorial alcohol. That is my preferred rationale.