60 | CHAPTER 2 Generalization: How Broadly Do the Results Apply? 41. Does the theory-based p-value appear to be a valid approximation of the simulated p- value for population 2 and this sample size? Explain how you are deciding. 42. Did the assumed shape of the population (Pop 1 vs. Pop 2) make a substantial difference on the distribution of sample means? Justify your answer. (Hint: Think about the shape, center, and variability of the sample means.) 2. Strength of evidence: 43. Did the assumed shape of the population (Pop 1 vs. Pop 2) make a substantial difference on the strength of evidence against the null hypothesis? Explain. So, in fact, the simulation-based method may not be all that sensitive to the shape of the population that we use. One advantage of the t-procedure is that we don't have to generate a population to sample from at all as long as the validity conditions are met. Follow-up #2 Earlier in this section we talked about the potential advantages of the median compared to the mean in summarizing quantitative variables when the distribution of the variable is skewed. However, we analyzed the strength of evidence with regards to a population mean. What if we used the median instead? 44. Restate the null and alternative hypotheses in terms of a population median of 8 hours. 45. Explain how you would modify the 35 strategy to test these hypotheses a. Statistic: What is the value of the new statistic? b. Simulate: How would you modify the simulation? (Hint: What information will you To enter special characters and collect from each random sample?) formatting, use "Ctrl+E" in Windows and "Cmd + E" in c. Strength of evidence: How would you modify your assessment of the strength of evidence