1) please make sure your answer is correct, Thank You So Much!

Question 1) (9 points) Suppose that there is a test prep company that states their program raises SAT scores by 90 points on average. You believe the real average difference is lower. To study this you randomly select 10 of their recent students and record their SAT score before and after the program (note: you may assume there were many students to choose from). You get the following results: SAT Score After 1330 1350 1540 SAT Score Before 1300 1280 1420 1070 1200 1130 1210 1250 1290 950 1030 1020 1070 1400 1560 1 190 1280 Student (a) Carry out a hypothesis test at a = .05 to test your claim that the average increase in SAT score is LESS than 90 points after this program. Make sure to conrm all necessary conditions. State your conclusion in context of the situation. (b) Build a 95% confidence interval for the average difference in SAT score before and after this program. Make sure to interpret your interval. (c) Would concluding that this program raises scores by less than 90 points on average when in reality they do raise scores by 90 points on average be a Type 1 or Type 2 error