Question

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 200 students who completed this core set of courses results in a mean math score of 20.5 on the college entrance exam with a standard deviation of 3.5. 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 math portion of the exam? Complete parts a) through d) below.

Answer 1

The results suggest that students who complete the core curriculum are ready for college-level mathematics.

Step-by-step explanation:

The results suggest that students who complete the core curriculum are ready for college-level mathematics. To determine this, we can use a hypothesis test. Based on the given information, the sample mean math score is 20.5, the population mean score for readiness is 20, and the standard deviation is 3.5. We can perform a one-sample t-test to compare the sample mean with the population mean.

To determine if the results suggest that students who complete the core curriculum are ready for college-level mathematics, we need to compare the sample mean math score to the population mean score. The hypothesis test will provide a p-value, which represents the probability that the sample mean is significantly different from the population mean.

Performing the hypothesis test, we assume that the null hypothesis is that the sample mean math score is not significantly different from the population mean score of 20. The alternative hypothesis is that the sample mean math score is significantly higher than the population mean score of 20. Using the given information, we calculate the t-statistic and the corresponding p-value. Based on the p-value, if it is below a certain threshold (usually 0.05), we can reject the null hypothesis and conclude that the results suggest students who complete the core curriculum are ready for college-level mathematics.