The ACT is a college entrance exam. In addition to administering this exam, researchers at ACT gauge high school students’ readiness for college-level subjects. For example, ACT has determined that a score of 22 on the mathematics portion of the ACT suggests that a student is ready for college-level mathematics. To achieve this goal, ACT recommends that students take a core curriculum of math courses in high school.

This core is 1 year of credit each in Algebra I, Algebra II, and Geometry. Suppose a random sample of 200 students who completed this core set of courses results in a mean ACT math score of 22.6 with a standard deviation of 3.9. Do these results suggest that students who complete the core curriculum are ready for college-level mathematics? That is, are they scoring above 22 on the math portion of the ACT?

(a) State the appropriate null and alternative hypotheses.

(b) Verify that the requirements to perform the test using the t-distribution are satisfied.

(c) Use the classical or P-value approach at the α = 0.05 level of significance to test the hypotheses in part (a).

(d) Write a conclusion based on your results to part (c).