Suppose you fit the multiple regression model Y = Po + Ptx1 + P2~2 + P3x3 + E to n = 30 data points and obtain the following result:

jj = 3.4 - 4.6~~ + 2.7~~ + .93x3 The estimated standard errors of p, and 3, are 1.86 and .29, respectively.

a. Test the null hypothesis H,: p, = 0 against the alternative hypothesis Hi,: P, # 0. Use a = .05.

b. Test the null hypothesis H,,: P, = 0 against the alternative hypothesis Ha: /3, # 0. Use a = .05

c. The null hypothesis H,: P2 = 0 is not rejected. In contrast, the null hypothesis H,,: P, = 0 is rejected.
Explain how this can happen even though pz > p3