The 2-methylcyclohexanol used in this experiment is a mixture of cis and trans isomers, approximately in 1:1 ratio. Which kind of mechanism can better account for the product mixture obtained from the dehydration of cis and trans-2-methylcyclohexanol mixture: E1, E2, or a combination of the two

E1

Explanation:

A detailed mechanism of the reaction is shown in the image attached obtained from UCSB.

We can see from the mechanism that the reaction occurs via a carbocation intermediate. The transition state involves a carbcation and this is only typical of an E1 mechanism.

Furthermore, there is a 1,2-hydride shift which leads to the formation of the more stable tertiary carbocation. The products clearly indicate a rearrangement and points towards an ionic mechanism in operation.