Suppose we have a dataset on high school students. Amongst the variables in this dataset are measures of cumulative grade point average ("cumgpa"), a dummy variable for gender (female=1 if the student is female, 0 otherwise), and a dummy variable for race (white=1 if the student is white, 0 otherwise).

We execute a few basic regressions for the dependent variable cumgpa and produce the following output in STATA:

.//Model 1 (coefficients only)

. regress cumgpa white if female==0

------------------------------------------------------------------------------

cumgpa | Coef. Std. Err. t P>|t| [95% Conf. Interval]

-------------+----------------------------------------------------------------

white | .1765394 .0592231 2.98 0.003 .060172 .2929067

_cons | 2.17771 .0505773 43.06 0.000 2.078331 2.277089

------------------------------------------------------------------------------

. //Model 2 (coefficients only)

. regress cumgpa white if female==1

------------------------------------------------------------------------------

cumgpa | Coef. Std. Err. t P>|t| [95% Conf. Interval]

-------------+----------------------------------------------------------------

white | .4949671 .1165576 4.25 0.000 .2646478 .7252865

_cons | 2.30963 .1056241 21.87 0.000 2.100915 2.518344

------------------------------------------------------------------------------

. //Model 3 (coefficients only)

. gen fem_white=female*white

. regress cumgpa female white fem_white

------------------------------------------------------------------------------

cumgpa | Coef. Std. Err. t P>|t| [95% Conf. Interval]

-------------+----------------------------------------------------------------

female | bbbbbbbb .1208802

white | aaaaaaaa .0585118

fem_white | cccccccc .1348207

_cons | dddddddd .0499699

------------------------------------------------------------------------------

Model 3 includes the variable Female and an interaction of Female and White (Fem_White). Some of the STATA output has been concealed. These values can be deduced from Models 1,2.

Suppose the result for ccccccc is .30 (it isn't). Given everything else on the printout is correct, what is the p-value for a hypothesis test that the coefficient on Fem_White=0? (Hint: there are enough observations for you to use the z-distribution in place of the t.)