Suppose you fit the model y = 0 + 1x1 + 2x2 + 3x3 + to n = 30 data points

Suppose you fit the model
y = β0 + β 1x1 + β 2x2 + β 3x3 + Ɛ
to n = 30 data points and obtain the following result:
ŷ = 3.4 - 4.6x1 + 2.7x2 + .93x3
The estimated standard errors of β2 and β3 are 1.86 and .29, respectively.
a. Test the null hypothesis H0: β2 = 0 against the alternative hypothesis Hα: β2 ≠ 0. Use α = .05.
b. Test the null hypothesis H0: β3 = 0 against the alternative hypothesis Hα: β2 ≠ 0. Use α = .05.
c. The null hypothesis H0: β2 = 0 is not rejected. In contrast, the null hypothesis H0: β3 = 0 is rejected. Explain how this can happen even though β2 > β3.