In an exam, we randomly chose some students who get both the pretest and the posttest. We are interested in the difference of the score of two test. Assume that the ¦Ò of score difference is 10 and the difference follows a normal distribution. If the H0 hypothesis is that there is no difference between the scores, and it is important to detect the H1 that the different score is 2.

Question

In an exam, we randomly chose some students who get both the pretest and the posttest. We are interested in the difference of the score of two test. Assume that the ¦Ò of score difference is 10 and the difference follows a normal distribution. If the H0 hypothesis is that there is no difference between the scores, and it is important to detect the H1 that the different score is 2. 
Please calculate the power for sample size of 10,20 and 50. Then determine how large the sample should be if we need this alternative with power of 0.8?  (¦Á=0.05)