Lei is a PhD student in sociology. She has a regression equation Yi =

a + bXi + Ziγ + i. Here, Xi is a scalar, while Zi is a 1×5 vector of control variables, and γ is a 5×1 vector of parameters. Her theory is that b = 0. She is willing to assume that the i are IID N (0, σ2), independent of X and Z. Fitting the equation to data for i = 1,..., 57 by OLS, she gets bˆ = 3.79 with SEˆ = 1.88. True or false and explain—

(a) For testing the null hypothesis that b = 0, t .

= 2.02. (Reminder:

the dotted equals sign means “about equal.”)

(b) bˆ is statistically significant.

(c) bˆ is highly significant.

(d) The probability that b = 0 is about 95%.

(e) The probability that b = 0 is about 5%.

(f) If the model is right and b = 0, there is about a 5% chance of getting |b/ˆ SE!| > 2.

(g) If the model is right and b = 0, there is about a 95% chance of getting |b/ˆ SE!| < 2.

(h) Lei can be about 95% confident that b = 0.

(i) The test shows the model is right.

(j) The test assumes the model is right.

(k) If the model is right, the test gives some evidence that b = 0.