To understand factors affecting snowfall size in Linköping in each December, researchers study snowfall size $Y$ in terms of temperature $x_{1}$ and moisture content $x_{2},$ by linear regression:

Y=\beta_{0}+\beta_{1}x_{1}+\beta_{2}x_{2}+\varepsilon,\quad\text{where }\varepsilon\sim N(0,\sigma^{2}).

To study such linear regression, researchers use a sample with sample size $n=16$ and the method of least squares to obtain: the estimated values $\hat{\beta}_{i}$ of $\beta_{i},$ together with their standard errors denoted as $se(\hat{\beta}_{i})$ or $s_{\hat{\beta}_{i}}:$

\hat{\beta}_{0}=1.58,\,\,se(\hat{\beta}_{0})=0.14;\qquad\hat{\beta}_{1}=8.12,\,\,se(\hat{\beta}_{1})=0.28;\qquad\hat{\beta}_{2}=0.08,\,\,se(\hat{\beta}_{2})=0.02.

Researchers want to examine whether or not snowfall size $Y$ really depends on moisture content $x_{2}.$ To this end, one wants to check whether or not $\beta_{2}\neq 0,$ based on the sample.