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. Part B: Create and interpret a 90% confidence interval for the difference in ACT scores between athletes and nonathletes.
Permutations and Combinations
If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.
Counting Theory
The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.
Twenty-five students from Harry High School were accepted at Magic University. Of those students, 10 were offered athletic scholarships and 15 were not. 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.
Part B: Create and interpret a 90% confidence interval for the difference in ACT scores between athletes and nonathletes.
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