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 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: = 50

H1:A < 50

a) Construct a 95% confidence interval for

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?