You are tasked to implement a randomized experiment in order to test the effectiveness (mea- sured in grade point averages,"GPA") of a new set of schooling material for high school students. At one high school, you are planning to randomly give the material to some subset of students, but not other students at that same school. From historic data (i.e. before the intervention) you know that the variance of the GPA score is equal to 1.3. The organization expects an increase in GPA scores of 0.1 due to the intervention. Assume that the treatment / control proportions are equal to 80% / 20%. How large does the sample size have to be in order to be able to distinguish an effect of this size from a null effect at the 95 percent level of confidence