Answer
There is statistical evidence that the weight loss was greater than zero.
But, notice that a weight loss of 1.6 kg within a year is a small weight loss. It might have been due to many others factors.
Work Step by Step
$H_0:~µ=0$ versus $H_1:~µ\gt0$
Requirement:
$n\geq30$
$n=79$, so:
$d.f.=n-1=78$
$t_0=\frac{x ̅-µ_0}{\frac{s}{\sqrt n}}=\frac{1.6-0}{\frac{5.4}{\sqrt {79}}}=2.634$
$t_α=t_{0.05}=1.664$
(According to Table VI, for d.f. = 80, the closest value to 78, and area in right tail = 0.05)
Since $t_0\gt t_α$, we reject the null hypothesis.
