State with reason whether the following statements are true, false, or uncertain. Be precise.

a. The t test of significance discussed in this chapter requires that the sampling distributions of estimators β̂₁ and β̂₂ follow the normal distribution.

b. Even though the disturbance term in the CLRM is not normally distributed, the OLS estimators are still unbiased.

c. If there is no intercept in the regression model, the estimated u_i (= û_i ) will not sum to zero.

d. The p value and the size of a test statistic mean the same thing.

e. In a regression model that contains the intercept, the sum of the residuals is always zero.

f. If a null hypothesis is not rejected, it is true.

g. The higher the value of σ², the larger is the variance of β̂₂ given in Eq. (3.3.1).

Eq (3.3.1) is:

var (β̂₂) = σ₂ / Σx_i²

h. The conditional and unconditional means of a random variable are the same things.

i. In the two-variable PRF, if the slope coefficient β₂ is zero, the intercept β₁ is estimated by the sample mean Y̅.

j. The conditional variance, var (Y_i | X_i) = σ², and the unconditional variance of Y, var (Y) = σ²_Y, will be the same if X had no influence on Y.