With n=20n=20n=20, β^1=2.5\hat{\beta}_1 = 2.5β^1=2.5, and SE(β^1)=0.5SE(\hat{\beta}_1) = 0.5SE(β^1)=0.5, test H0:β1=0H_0: \beta_1 = 0H0:β1=0 at the 5% significance level.
Reject H0H_0H0; t=5t=5t=5 exceeds critical value ≈2.10\approx 2.10≈2.10
Fail to reject; t=5<2.10t=5 < 2.10t=5<2.10
Reject H0H_0H0; t=2.5t=2.5t=2.5 exceeds critical value
Cannot test without knowing σ2\sigma^2σ2