Suppose you fit the multiple regression model y = 0 + 1x1 + 2x2 + 3x3 +

Suppose you fit the multiple regression model
y = β0 + β1x1 + β2x2 + β3x3 + ε
to n = 30 data points and obtain the following result:
 = 3.4 - 4.6x1 + 2.7x2 + .93x3
The estimated standard errors of 2 and 3 are 1.86 and .29, respectively.
a. Test the null hypothesis H0: β2 = 0 against the alternative hypothesis Ha: β2 ≠ 0. Use α = .05.
b. Test the null hypothesis H0: β3 = 0 against the alternative hypothesis Ha: β3 ≠ 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 2 > 3.