SAT scores: The College Board reports that in 2009, the mean score on the math SAT was 582 and the population standard deviation was =σ120. A random sample of 20 students who took the test in 2010 had a mean score of 515. Following is a dotplot of the 20 scores. (a) Are the assumptions for a hypothesis test satisfied? Explain. (b) If appropriate, perform a hypothesis test to investigate whether the mean score in 2010 differs from the mean score in 2009. Assume the population standard deviation is =σ120. What can you conclude? Use the =α0.10 level of significance and the critical value method.