**11. Correct. The answer is false**

Let us use subscripts 1 and 2 for classes X and Y respectively, so that

(estimated s_{1}^{2})=s_{1}^{2}n_{1}/(n_{1}-1)=10^{2}*16/15=106.67, and

(estimated s_{2}^{2})=s_{2}^{2}n_{2}/(n_{2}-1)=13^{2}*25/24=176.04.

Given:

H_{0}:
σ_{1}^{2}= σ_{2}^{2}

Ha: σ_{1}^{2}>
σ_{2}^{2}, thus the decision rule must be based on the
one-tailed F distribution.

F=(estimated σ_{2}^{2})/(estimated
σ_{ 1}^{2})=1.65.

The number of degrees of freedom
of the numerator is n_{2}=25-1=24
and the number of degrees of freedom of the denominator is n_{1}=16-1=15.
At the 0.01 level for 24, 15 degrees of freedom F_{0.99}=3.29. Since
F< F_{0.99} we fail to reject H_{0} at 0.01 significance
level.