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1. Consider the following table that lists SAT scores before and after a sample of five students . took a preparatory course. Student 2 3 SAT score before course 700 840 830 360 690 SAT score after course 720 820 900 700 (a) (2 pts.) State the correct hypotheses to test the affectiveness of the course in improving the SAT scores. Ho : Ha : (b) (2 pts.) In the context of the problem, explain Type I error and Type II error. Type I Error: Type II Error: (c) (5 pts.) Find the value of the standardized test statistic. (d) (3 pts.) Find the rejection region at a = .05