The Dean of Instruction at a local college requested that a new standardized test for an introductory statistics course be developed with the requirement that it should have µ = 120 points and σ = 15. A class of 30 students complete the new test with a mean grade of 115. Conduct a hypothesis test at α = .05 to determine whether the claim that µ = 120 can be supported. Use the p-value approach and complete the following to show how this would be done. a. What are the assumptions that need to be satisfied in order to use a t-test to test the significance of an observed difference between a known population mean and the mean of a set of sample data?

b. Summarize the similarities and differences between the critical value approach and the p-value approach to hypothesis testing.

c. Given a statistically significant outcome, why is the alternative hypothesis said to be "supported" but is not said to be "proven."

d. Why does "statistical significance" not necessarily also indicate "practical significance"? What is the difference between them?

e. Describe a scenario where a one-sample test of a population proportion could be used to answer a research question. Provide a brief summary of the scenario and state the null and alternative hypotheses in words and symbols.

Thank you so much!