A college entrance test company determined that a score of 21 on the mathematics portion of the test 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 21.4 on the college entrance test with a standard deviation of 3.4. Do these results suggest that students who complete the core curriculum are ready for college-level mathematics? That is, are they scoring above 21 on the math portion of the test? Complete parts a) through d) below.
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.
c) Use the P-value approach at the alpha (α) equals 0.05 level of significance to test the hypotheses in part (a). Identify the test statistic. Identify the P-value.
d) Write a conclusion based on the results. Choose the correct answer below.
Reject the null hypothesis and claim that there is sufficient evidence to conclude that the population mean is greater than 21.