In equation (10), is a random error; there is a for each state. Gibson finds

In equation (10), δ is a random error; there is a δ for each state. Gibson finds that βˆ

1 is statistically insignificant, while βˆ

2 is highly significant

(two-tailed). Suppose that Gibson computed his P-values from the standard normal curve; the area under the curve between −2.58 and +2.58 is 0.99. True or false and explain—

(a) The absolute value of βˆ

2 is more than 2.6 times its standard error.

(b) The statistical model assumes that the random errors are independent across states.

(c) However, the estimated standard errors are computed from the data.

(d) The computation in

(c) can be done whether or not the random errors are independent across states: the computation uses the tolerance scores and repression scores, but does not use the random errors themselves.

(e) Therefore, Gibson’s significance test s are fine, even if the random errors are dependent across states.