A college entrance exam company determined that a score of 20 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 20.6 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 20 on the mathematics portion of the exam? Complete parts a) through d) below.
a) State the appropriate null and alternative hypotheses. Fill in the correct answers below.
The appropriate null and alternative hypotheses are $\mathrm{H}_{0}: \nabla \nabla \nabla$ versus $\mathrm{H}_{1}: \nabla \nabla \nabla \square$.
Answer
\( \boxed{H_0: \mu = 20 \text{ versus } H_1: \mu > 20} \)
Step 1 ：The null hypothesis is a statement of no effect or no difference. In this case, it would be that the mean score is equal to 20, which is the score suggesting readiness for college-level mathematics.
Step 2 ：The alternative hypothesis is what we are trying to find evidence for. In this case, it would be that the mean score is greater than 20, indicating that students who complete the core curriculum are ready for college-level mathematics.
Step 3 ：Set up the null hypothesis as \( H_0: \mu = 20 \)
Step 4 ：Set up the alternative hypothesis as \( H_1: \mu > 20 \)
Step 5 ：\( \boxed{H_0: \mu = 20 \text{ versus } H_1: \mu > 20} \)
