1. The authors of the SAT want to estimate the difficulty level of the math test. They administer the test to 41 randomly-selected students (from among those who have registered to take the SAT). The average score in the sample is 502. Assume that scores on the math SAT are approximately normally distributed, and that the population standard deviation is 50 points. a. Give the 99% confidence interval for the population mean math SAT score (which may be interpreted as the true difficulty level of the test). b. The SAT authors are aiming for a population mean score of 525. In a hypothesis test, their null hypothesis is Ho: u = 525, and the alternative hypothesis is HA: u # 525. Using the confidence interval approach, what is the conclusion of this hypothesis test, at the 1% level of significance? Explain. c. What is the p-value? d. Suppose that the SAT authors want the confidence interval to be no longer than 10 points. What is the minimum sample size they can use