Using margins, test, and lincom to test hypothesis that two predictive values are equal

Hi,
I'm trying to do something that should be easy but I'm not certain I am doing it/interpreting the output the correct way.

My basic model is a mixed level model and I am interested in the independent variables AC, CP, and their interaction. Specifically, I am predicting that CP will be a significant predictor of DV when AC is low, but that CP will become irrelevant when AC is high.

Thus, I run the following:

Code:

mixed DV X Y AC##CP || Country: || ParticipantID:

(deleted since question is about the next step)

 margins, at( AC=(1 7) CP=(40 70)    ) post



Predictive margins                              Number of obs     =      7,243

Expression   : Linear prediction, fixed portion, predict()

1._at        : AC              =           1
                   CP              =          40

2._at        : AC              =           1
                  CP               =          70

3._at        : AC              =           6
                CP                 =          40

4._at        : AC              =          6
                 CP                  =          70

------------------------------------------------------------------------------
             |            Delta-method
             |     Margin   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         _at |
          1  |  -.0126381   .1316229    -0.10   0.924    -.2706142    .2453381
          2  |   .0034672   .1128805     0.03   0.975    -.2177744    .2247088
          3  |  -.0421888   .1166925    -0.36   0.718    -.2709019    .1865243
          4  |  -.0267793   .1119971    -0.24   0.811    -.2462896    .1927309
------------------------------------------------------------------------------


 test 3._at=4._at

 ( 1)  3._at - 4._at = 0

           chi2(  1) =    0.01
         Prob > chi2 =    0.9072


. lincom 3._at - 4._at

 ( 1)  3._at - 4._at = 0

------------------------------------------------------------------------------
             |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         (1) |  -.0154094   .1321867    -0.12   0.907    -.2744906    .2436717
------------------------------------------------------------------------------




In case it is relevant:

sum AC CP

    Variable |        Obs        Mean    Std. Dev.       Min        Max
-------------+---------------------------------------------------------
          AC |     18,887    4.062194    1.136002          1          6
          CP |     23,302    57.39825    15.30319         25         88

So my questions:

First, am I correct in interpreting the test and lincom results to say that the probability that the predictive values for 3._at and 4._at are not equal to one another is (1-.907=.093)? In other words, if we consider the null hypothesis to be that 3._at is not equal to 4._at, then the p-value of the test would be .093?

Second, is there a better way to test the hypothesis that the importance of the CP interactive term declines to zero with an increase in AC?