Suppose you fit the model y = b0 + b1 x1 + b2 x2 + b3 x3 + e to n = 30 data points and obtain the following result:

yn = 2.2 - 2.8x1 + 1.9x2 + .97x3 The estimated standard errors of b n 2 and b n 3 are 1.06 and .27, respectively.

a. Test the null hypothesis H0: b2 = 0 against the alternative hypothesis Ha: b2  0. Use a = .05.

b. Test the null hypothesis H0: b3 = 0 against the alternative hypothesis Ha: b3  0. Use a = .05.

c. The null hypothesis H0: b2 = 0 is not rejected. In contrast, the null hypothesis H0: b3 = 0 is rejected. Explain how this can happen even though b n 2 7 b n 3?