Investigation Chapter 3: Faking Cell Phone Calls Have you ever pretended to be talking on your cell phone in order to avoid interacting with people around you? Is faking cell phone calls a common practice among cell phone users? A recent survey conducted by the Pew Research Center during April 26 - May 22, 2011 asked cell phone users about this issue and many others regarding the respondents' cell phone usage in the past 30 days. The survey involved selecting a random sample of 1,858 American cell phone users. 1. Was the sample random? 2. Was the sampling method unbiased? 3. Do you feel comfortable generalizing your conclusions to all cell phone users? If not, is there a broader population you feel you can generalize your conclusions to? Suppose instead your data came from a random sample of 1,858 college students. 4. Was the sample random? 5. Was the sampling method unbiased? 6. Do you feel comfortable generalizing your conclusions to all cell phone users? If not, is there a broader population you feel you can generalize your conclusions to? Now suppose you asked 1,858 people walking on Wall Street throughout the day on a Monday. 7. Was the sample random? 8. Was the sampling method unbiased? 9. Do you feel comfortable generalizing your conclusions to all cell phone users? If not, is there a broader population you feel you can generalize your conclusions to? A reporter for International Business Times took the Pew survey results and wrote that more than 1 in 10 cell phone users in the U.S. has engaged in such fake cell phone use in the past 30 days. Notice that the reporter's claim is about the population of all cell phone users in the U.S. In the following questions, we will investigate whether the survey results provide evidence that more than 1 in 10 cell phone users have faked cell phone calls in the last 30 days. Step 1: Ask a research question 10. What is our research question? Step 2: Design a study and collect data 11. What are the observational units? 12. What is the variable that is measured/recorded on each observational unit? 13. Describe the parameter of interest in words. (You can use the symbol to represent this parameter.) 14. State the appropriate null and alternative hypotheses to be tested. Of the 1,858 cell phone users, 13% admitted to faking cell phone call in the past 30 days. 15. If another sample of 1,858 American cell phone users were surveyed, could the percent admitting to faking cell phone calls in the past 30 days, change? Explain your reasoning. Step 3: Explore the data 16. Is the 13% a statistic or a parameter? How are you deciding? Step 4: Draw inferences Let's use the 3S strategy to help us investigate how much evidence the sample data provide to support the conjecture more than 1 in 10 cell phone users fake cell phone calls. Statistic 17. What is the statistic that you can use to summarize the data collected in the study? Simulate 18. If we assume that the population proportion of cell phone users who fake cell phone calls is actually 0.10. Is it possible that we could observe the statistic we did from this sample of 1858 cell phone users? Why? . 19. Use the One Proportion applet to simulate 1000 repetitions of this study, assuming that the proportion of cell phone users who fake calls is 0.10. Report what values you input into the applet. 20. What is the center of your simulated null distribution? Does it make sense that this is the center? Explain. 21. Are there any values of simulated sample proportions that are less than 0.10? Are there any values of simulated sample proportions that are greater than 0.10? What does that tell you? Strength of evidence 22. Based on the null distribution generated using the 1000 simulated values of the statistic, what values would you consider typical values and what would you consider atypical values of the statistic? 23. How do the actual study results compare to the null distribution obtained when simulating assuming 0.10 of the population faked cell phone calls? Do you believe the study results provide convincing evidence against the \"1 in 10 cell phone users fake cell phone calls\" null hypothesis and in favor of the \"more than 1 in 10 cell phone users fake cell phone calls\" alternative hypothesis? Why or why not? 24. Determine the approximate p-value from your simulation analysis. Also interpret what this p-value represents (i.e., the probability of what, assuming what?). Step 5: Formulate conclusions 25. Now, let's step back a bit and think about the scope of our inference. What are the wider implications? Do you think that your conclusion holds true for people in general? What is the broader population we are able to generalize to? It is important to remember how we gathered our data to answer these questions. Step 6: Look back and ahead 26. Summarize your findings. If you were to repeat this study, would you gather your sample in a different way? Are there things about the study you would change? What further research might you follow up with from what you have learned in this study