Answer
The null hypothesis is not rejected, this means that there is no sufficient evidence to conclude that the mean height differs from 6.698 feet.
Work Step by Step
Given that, $\mu=6.698, \bar x=6.75, \sigma =5.5\;\text{inches}\approx 0.458333 \;\text{feet}, n=30,$ then,
The null and alternative hypotheses are
$H_{0}: \mu=6.698.\\H_{1}: \mu\ne 6.698.$
at $\alpha=0.05, Z_{0.025}=1.96, \text{so the critical region is}\;R-[-1.96,+1.96]$
and
$z=\frac{\bar x-\mu}{\frac{\sigma}{\sqrt{n}}}=\frac{6.75-6.698}{\frac{0.458333}{\sqrt{30}}}\approx 0.62$
Since $z=0.62$ falls within a non-critical region, the null hypothesis is not rejected.
