Question

Twenty-five students from Harry High School were accepted at Magic University. Of those students, 10 were offered athletic scholarships and 15 were not. Mrs. Hermione believes Magic University may be accepting people with lower ACT scores if they are athletes. The newly accepted student ACT scores are shown here.

Athletic scholarship: 16, 24, 20, 25, 24, 23, 21, 22, 20, 20
No athletic scholarship: 23, 25, 26, 30, 32, 26, 28, 29, 26, 27, 29, 27, 22, 24, 25

Part A: Do these data provide convincing evidence of a difference in ACT scores between athletes and nonathletes? Carry out an appropriate test at the α = 0.10 significance level. (5 points)

Part B: Create and interpret a 90% confidence interval for the difference in ACT scores between athletes and nonathletes. (5 points)

Answer 1