The national mean sat score in math is 550. suppose a high school principal claims that the mean sat score in math at his school is better than the national mean score. a random sample of 72 students finds a mean score of 574. assume that the population standard deviation is latex: \sigma=100 σ = 100 . is the principal's claim valid? use a level of significance of latex: \sigma=0.05 σ = 0.05 .