Answer
The events "45-54" and "more likely" are not independent because $P(45–54~|~more~likely)\ne P(45–54)$
Work Step by Step
The sample space: 2160 adult Americans. So, $N(S)=2160$
According to the marginal distribution (see page 235) of the third column: $N(45–54)=546$
Using the Empirical Approach (page 258):
$P(45–54)=\frac{N(45–54)}{N(S)}=\frac{546}{2160}=\frac{91}{360}\approx0.2528$
According to the marginal distribution (see page 235) of the first row: $N(more~likely)=1329$
According to the cell in the first row, third column: $N(45–54~and~more~likely)=360$
$P(45–54~|~more~likely)=\frac{N(45–54~and~more~likely)}{N(more~likely)}=\frac{360}{1329}=\frac{120}{443}\approx0.2709$
$P(45–54~|~more~likely)\ne P(45–54)$
The events "45-54" and "more likely" are not independent (see definition on page 292).
