Question

In many colleges and universities around the country, educators are changing their approach to instruction from a "teacher/lecture-centered model" to a "student-centered model" where students learn in a laboratory environment in which lecture is not emphasized and students can proceed at a pace suitable to their learning needs. In one school where this model was being introduced, of the 743 students who enrolled in the traditional lecture model, 364 passed; of the 567 in the student-centered model, 335 passed. Does the evidence suggest that the student-centered model results in a higher pass rate than the traditional model? Use the 0.01 level of significance.

What are we looking for and what are we going to do with this?

Answer 1

To assess if the student-centered model has a higher pass rate, a hypothesis test for two proportions is conducted. The null hypothesis assumes no difference, and the alternative hypothesis suggests a higher rate for the student-centered model. A statistical test will compare the models' pass rates, and if the resulting p-value is less than 0.01, the null hypothesis is rejected.

Step-by-step explanation:

To determine whether the student-centered model results in a higher pass rate than the traditional lecture model at the 0.01 level of significance, we will perform a hypothesis test for two proportions. Here's the process:

• State the null hypothesis (H0): There is no difference in pass rates between the two models.
• State the alternative hypothesis (H1): The student-centered model has a higher pass rate.
• Calculate the pass rate for each group: Traditional (364/743) and Student-Centered (335/567).
• Use a statistical test (e.g., Z-test for two proportions) to determine if the difference in pass rates is significant.
• Compare the p-value from the test to the level of significance (0.01). If the p-value is less than 0.01, reject the null hypothesis in favor of the alternative.

This method will provide evidence on whether the student-centered model is statistically more effective at the given level of significance. It's important to note that even if the student-centered model shows a higher pass rate, this could be influenced by other factors that are not controlled for in the comparison.