11. Correct. The answer is false
Let us use subscripts 1 and 2 for classes X and Y respectively, so that
(estimated s12)=s12n1/(n1-1)=102*16/15=106.67, and
H0: σ12= σ22
Ha: σ12> σ22, thus the decision rule must be based on the one-tailed F distribution.
F=(estimated σ22)/(estimated σ 12)=1.65.
The number of degrees of freedom of the numerator is n2=25-1=24 and the number of degrees of freedom of the denominator is n1=16-1=15. At the 0.01 level for 24, 15 degrees of freedom F0.99=3.29. Since F< F0.99 we fail to reject H0 at 0.01 significance level.