A company advertises that by using their SAT math prep class, students can increase their score by at least 50 points, A teacher is skeptical of this claim. Suppose mu represents the actual mean increase in math SAT scores of the population who have used the method and assume the distribution of their scores is approximately normal. The teacher collects a data sample of 16 students who took the class to see if the claim is true. The mean increase of scores is 45 points with a standard deviation of 20 points. Is this data enough evidence that the mean improvement is less than 50 points?

H0:mu = 50
H1:Amu< 50

-The above data are the differences in SAT scores obtained by a student before the training and after the training. What is this an ex of?
-What are the appropriate degrees of freedom for this test?