A principle at a certain high school claims that the students in her school are above average in SAT. She collects a random sample of 50 students and given an SAT test that provided with a mean score of 541. Is there sufficient evidence statistically to support the principal’s claim? The mean population SAT score is 500 with a standard deviation of 100. SAT scores are normally distributed. Please show all the steps involved in a hypothesis testing including proper statistical symbols, formula used, and report/interpret results in complete sentences.