A company advertises that by using its SAT math prep class, students can increase their score by at least 50 points, A teacher is skeptical of this claim. Suppose μ 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:μ = 50 

H1:Aμ < 50 

a) Construct a 95% confidence interval for μ

b) The about data are the differences in SAT scores obtained by a student before the training and after the training. What is this an example of?