INVESTIGATION: FAKING CELL PHONE CALLS

Have you ever pretended to be talking on your cell phone in order to avoid interacting with peo- ple 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. Doyoufeelcomfortablegeneralizingyourconclusionstoallcellphoneusers?Ifnot,isthere a population (broader than the sample) you feel you can generalize your conclusions to?

Suppose instead your data came from a random sample of 1,858 college students.

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 population you feel you can generalize your conclusions to?

Now suppose you asked 1,858 people walking on Wall Street (in New York City) throughout the day on a Monday.

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 population you feel you can generalize your conclusions to?
4. A reporter forInternational Business Timestook 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.

1. What are the observational units?
2. What is the variable that is measured/recorded on each observational unit?
3. Describe the parameter of interest in words. (You can use the symbolto represent this parameter.)
4. State the appropriate null and alternative hypotheses to be tested.

Of the 1,858 cell phone users, 13% admitted to faking cell phone calls in the past 30 days.

15.If another sample of 1,858 American cell phone users were surveyed, could the percentage 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 that more than 1 in 10 cell phone users fake cell phone calls.

INVESTIGATION:Faking Cell Phone Calls161

162CHAPTER 2

Generalization: How Broadly Do the Results Apply?

Statistic

17.What is the statistic that you can use to summarize the data collected in the study?Simulate

1. 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 1,858 cell phone users? Why?
2. Use theOne Proportionapplet to simulate 1,000 repetitions of a random process, assum- ing that the proportion of cell phone users who fake calls is 0.10. Report what values you input into the applet.
3. What is the center of your simulated null distribution? Does it make sense that this is the center? Explain.
4. Arethereanyvaluesofsimulatedsampleproportionsthatarelessthan0.10?Arethereany values ofsimulatedsample proportions that are greater than 0.10? What does that tell you?

Strength of evidence

1. Based on the null distribution generated using the 1,000 simulated values of the statis- tic, what values would you consider typical values and what would you consider atypical values of the statistic?
2. How do the actual study results compare to the null distribution obtained when simu- lating 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?
3. 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?