population std deviation=12
* compute the power of the hypothesis test if the program has a 3-point effect.
I came up with 83.88 %]
[ i got this by mulitiping the z-core of 1.96+(78)*2
then i found the propotion which was .08388*10=83.88%
Based on your critical value of 1.96 and alpha level (0.05), one important area that you're missing, in terms of computing power, is that you have to consider both sides of the standard normal pdf. In short, the null hyposthesis is two sided.
The other thing you have incorrect is that you have to multiply the z-score by the standard error (12/Sqrt[N]) and then add Mu.