Question

a college entrance exam company determined that a score of 24 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 250 students who completed this core set of courses results in a mean math score of 24.6 on the college entrance exam with a standard deviation of 3.7. do these results suggest that students who complete the core curriculum are ready for college - level mathematics? that is, are they scoring above 24 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 ( h_0 ) versus ( h_1 )

Explanation:

Step1: Determine the null hypothesis

The null hypothesis \(H_0\) is a statement of no - difference or no - effect. In the context of a one - sample mean test, it is usually a statement about the population mean \(\mu\). Here, the company's initial claim (the status quo) is that the mean score is \(24\). So, \(H_0:\mu = 24\).

Step2: Determine the alternative hypothesis

The alternative hypothesis \(H_1\) is what we are trying to find evidence for. The question is "Do these results suggest that students who complete the core curriculum are scoring above \(24\)". So, \(H_1:\mu>24\).

Answer:

The appropriate null and alternative hypotheses are \(H_0:\mu = 24\) versus \(H_1:\mu>24\).