Given that for SAT scores, = 500 and = 100: a. Test the claim of students at Bigbrain University that they have SAT

Given that for SAT scores, μ = 500 and σ = 100:

a. Test the claim of students at Bigbrain University that they have SAT scores that are statistically significantly higher than the ordinary population, because a random sample of 25 of their students averaged 530 on this test. Make your statistical decision by comparing the z score for the Bigbrain sample with the appropriate critical value for a two-tailed test. Would a one-tailed test be significant in this case? Would it be justified?

b. Repeat part (a) for a random sample of 64 students, who also have a mean of 530 on the SAT.