Answer
$-t_{\frac{α}{2}}\lt t_0\lt -t_{\frac{α}{2}}$: null hypothesis is not rejected.
There is not enough evidence to conclude that a linear relation exists between calories and sugar content.
Work Step by Step
$H_0: β_1=0$ versus $H_1: β\ne0$
$t_0=\frac{b_1}{s_{b_1}}=\frac{−0.0146}{0.05479}=-0.266$
$n=14$, so:
$d.f.=n-2=12$
$t_{\frac{α}{2}}=t_{0.005}=3.055$
(According to Table VI, for d.f. = 12 and area in right tail = 0.005)
Also, $-t_{\frac{α}{2}}=-3.055$
Since $-t_{\frac{α}{2}}\lt t_0\lt -t_{\frac{α}{2}}$, we do not reject the null hypothesis.
