A college entrance exam company determined that a score of 23 on the mathematics portion of the exam suggests that a student is
ready for college-level mathematics. To achieve this goal, the company recommends that students take a core curriculum of math courses in high school. Suppose a random sample of 150 students who completed this core set of courses results in a mean math score of 23.6 on the college entrance exam with a standard deviation of 3.3. Do these results suggest that students who complete the core curriculum are ready for college-level mathematics? That is, are they scoring above 23 on the math portion of the exam? Complete parts a) through d) below. Required:
a. State the appropriate null and alternative hypotheses.
b. Verify that the requirements to perform the test using the t-distribution are satisfied. Check all that apply.
A. The students were randomly sampled.
B. The sample size is larger than 30.
C. The students' test scores were independent of one another.
D. None of the requirements are satisfied.
c. Use the P-value approach at the α= 0.05 level of significance to test the hypotheses in part (a).
d. Write a conclusion based on the results.
