Question: A math teacher claims that she has developed a review course that increases the scores of students on the math portion of the SAT exam. Based on data from The College Board, the SAT math scores are normally distributed with a mean of 515 (µ) and a standard deviation of 114 ( \(\sigma \) ). The teacher obtains a random sample of 1800 students and puts them in the review class. She finds that the mean SAT math scores for the students in the sample is 519. Test the math teacher’s claim at \(\alpha =0.01\). Show all steps (by hand) including the hypotheses to receive full credit. After you have stated your conclusion, indicate which type of error could have been made and if possible, state the probability of making that error.